Stars do not simply disappear in death. In their deaths they join in as much in the life-cycle of the galaxy as they did during their prime. In their demise lies the seeds of the next generation of stars and planets.
On their way to death stars go through stages that are clear signals of impending disaster. One of these phases are the periodic oscillations of a star. All stars have variable brightness at some level. But some stars change their brightness to an extent that is obvious even from large distances. A subset of these stars vary their brightness over constant time intervals. These stars are called periodic variables. Some of these are binary stars but others are stars genuinely changing their brightness over time. The first such stars discovered were the cepheids, recognized to be periodic variables by Henrietta Leavitt. She also realized that the time period of the variation of brightness of the star was related to its intrinsic luminosity. This is referred to as the period-luminosity relation of cepheids. Cepheids have periods ranging from a day to hundreds of days. Harlow Shapley used this relation to tell the distance to globular clusters after he identified what he thought were cepheids in globular clusters. It was later realized that what he'd seen were not cepheids but RR Lyrae stars. These were periodic variables with periods smaller than cepheids, being around fractions of a day. Moreover they did not fall on the same line as the cepheids in the period luminosity relationship. Instead as we move towards increasing periods the line corresponding to RR Lyrae stars join up with the W Virginis stars. They have a period luminosity relationship that falls in a line parallel to that of cepheids, but is of a systematically lower brightness. Cepheids are population I stars that are young, where as W Virginis and RR Lyrae stars are from the population II stars that are old. Looking at the Hertzsprung-Russell diagram of the periodic stars they are all to be found in a thin strip roughly parallel and to the left of the giant branch called the instability strip. Stars turn variable when they enter this instability strip. Light stars enter the strip the first time when they are falling down from the giant branch after helium flash getting ready to settle onto the horizontal branch, when they turn into RR Lyrae stars. And a second time when they have exhausted the helium at their center and is climbing on the way back to the giant branch. This time they become the W Virginis stars. Heavier stars on the other hand cross the instability strip on their way to the giant branch from the main-sequence, burning helium. They on crossing the instability strip become cepheid stars. Now because both the W Virginis stars and the cepheids are giants, they have similar radii. But they are of widely differing masses. Consequently they have very different densities. The period of oscillation is related to the inverse square-root of the density. Higher the density shorter the period (i.e., shorter the time period between brightness peaks). So cepheids being the heavier stars and higher density have, at the same brightness, shorter time periods. This means that for stars with the same period of oscillation, cepheids will be systematically brighter than the W Virginis.
The fundamental reason why stars vary their brightness periodically is because they change their radius. This can be measured from the blue and redshift of the spectral lines from the star's surface. This is why periodic stars were first thought to be binary stars. But the variation of brightness and speed of the surface are not consistent with a binary and Harlow Shapley suggested that they were stars whose size changed periodically. The details of the process is quite complicated, but the basic phenomenon can be understood. The energy produced in stars is generated by nuclear fusion in the centers of stars. This energy gradually leaks out of the center heating up the star. The ability of a gas shell to be able to absorb the radiation falling on it is its opacity. If the opacity of the gas shell is high, it absorbs a lot of light. This heats the shell causing it to expand. So the surface of the star expands. As it expands the star becomes a lot brighter. However as the star's surface expands the gas shells become less dense. Consequently their opacity drops and they let through a lot of the light. This cools them down and causes them to shrink in size. As the star's surface shrinks it dims. Its density and opacity also increase and the star can go through the whole process again. It stands to reason that brighter stars should have longer periods of variation, because brighter stars also have larger radii. Which means larger distances to travel before appreciable changes are apparent in the size of the star. Hence it takes longer for the brightness to change.
The periodic oscillations is the indications of the imminent death of stars. But the nature of death for the star depends on its weight. In case of light stars the death comes relatively quietly although not invisibly. In case of heavier stars the death is one of the most spectacular events in the Universe.
Light stars start burning their helium late, starting abruptly in the helium flash. It goes through the instability strip twice, once on its way to the horizontal branch and once on its way back to the giant branch after exhausting all its helium. During this time there are no irrevocable changes, but gradually the expansion of star's surface become more and more violent. As the surface expands to huge distances it cools down enough for small dust particles to form in the gas clouds on the star's surface. These dust particles add to the opacity of the cloud. So even when the cloud is extended it stays too opaque to stop expanding and start to collapse. And at some stage it expands to a point that it is detached from the star altogether and is lost to the star in a stellar wind. The star keeps going through this losing of its surface until all the atmosphere around the core of carbon and oxygen is lost and the naked core is visible. This state with the visible core and the gas distributed around it is called a planetary nebula. The gas keeps expanding until it mixes with the rest of the Galaxy's gas and we are left with a hot shiny core of carbon and oxygen called the white dwarf. When the carbon and oxygen core left from the helium burning cannot burn it collapses getting hotter and denser. At these high temperatures of course the electron is torn from the atom (i.e., the atom is ionized) and the electrons act like free agents unanchored from the nuclei. Now electrons are loners refusing to be too close together. If they do happen to be together they better be parting company going their different ways. Now as gravity squeezes the star's core smaller the electrons are forced to occupy a smaller volume. This forces the electrons to try and escape this volume by moving faster. This opposes the pull of gravity trying to make the star's core smaller. And the star can again balance against the pull of gravity, even without burning nuclear fuel. However it does so by becoming incredibly small although it is very hot. Its mass is roughly that of the Sun, but its size is not much bigger than the Earth. Because it is hot it is white but because it is small it is dim, hence white dwarf. It radiates away its heat gradually cooling down until it ends up as dark cinder, signalling the death of the star.
Now one of the features of the electron gas in this particular state is that unlike ordinary gas, its temperature does not increase as the pressure is increased. So if more material is dumped onto the white dwarf, gravity squeezes harder, and pressure increases (as the electrons resist being pressed together) until they can balance each other. But the temperature of the electrons (the energy in their random motion) doesn't increase. So the white dwarf ends up smaller with increased gravity since it can't get hotter and expand like a ordinary star would. This means as more material is dumped onto the white dwarf it will get smaller with a more intense gravitational field. This will continue until the gravity gets so intense that even the resistance of the electrons to being pressed together cannot oppose it. The white dwarf will collapse under its own gravity. This means that there is a largest mass a white dwarf can have. If a white dwarf gets heavier than that mass it will collapse under its own weight. This mass limit is called Chandrashekhar mass limit after its discoverer Subramaniam Chandrashekhar.
One way in which white dwarf stars can acquire mass is by accreting mass from a companion in a binary star. In binary systems one star will, most likely, be more massive than the other. This means that it will evolve faster than the other. If it is a light star it will end up as a white dwarf, while the other star is still an ordinary star (because it is still lighter). Now in isolation the surface of a star is very nearly a perfect sphere. But if there is a gravitating companion nearby, like the white dwarf, then it will raise tides on the star's surface. This worsens when the companion star becomes a red giant and expands. The tidal effect of the white dwarf on the red giant causes it to distend into the shape of a spout that pours out material from the surface of the red giant onto the white dwarf. This material doesn't fall directly onto the surface of the white dwarf but forms a rotating disk around the white dwarf. The gas in this disk heats up in the effort to stay out of the dwarf and radiates light that can be observed. However none of this effort is of much use as the gas eventually does fall onto the white dwarf. This can lead to two different eventualities depending on the rate at which the companion red giant is losing material to the white dwarf.
If the rate of material gained by the white dwarf is slow, then the material gradually accumulates on the dwarf's surface raising the pressure and temperature (remember the material falling on the white dwarf is the ordinary gas from the companion's surface and not the electron gas that makes up the white dwarf itself). At some point the falling material gets hot and dense enough for nuclear fusion to ignite in the accumulated material. The dwarf's surface lights up in one intense burst of light and energy producing a nova. A new star appears in the sky and stays there for the time it takes for the white dwarf to process all the accumulated material. After its hour of glory (that is how long the star takes to reach its peak brightness) it returns in a few days to weeks to its original obscurity accumulating material until the next explosion. However it is not all obscure. Following the use of X-ray detectors binary systems with a red giant in the process of being cannibalized by the white dwarf have been observed through the radiation given off by the hot disk.
In case the rate of accumulation of material by the white dwarf is fast, the results are far more drastic. The material piles on the dwarf so fast it doesn't get any chance to burn it off. The material heats up and its pressure increases. The white dwarf under it is squeezed by the weight of the accumulating material until the Chandrashekhar limit is reached. Then the carbon/oxygen fossil from the star that died suddenly comes alive, ready to enter nuclear fusion. The entire dwarf catches fire, burning the nuclear fuel at a furious pace. The white dwarf explodes in an orgy of nuclear burning, producing a Type I Supernova. It is believed that this explosion is so severe that nothing is left behind, everything burns up and is flung back to the inter-stellar material. The star that started off by accumulating in clouds of inter-stellar material returns all of itself back to the inter-stellar material. But it doesn't return what it started off with. All through its life it has been processing the material that it first formed out of. As it slowly burns itself out the star converts pristine material from the clouds into heavier elements. Elements like oxygen, carbon, silicon that although small in amount compared to hydrogen is essential to the formation of planets and indeed of life. More importantly it is essential for the formation of more molecular clouds that will form the next generation of stars that will go through the whole cycle again. Single, lonely stars like the Sun will keep most of the heavy elements it produced locked up in itself dying without ever returning all it made through its life to the inter-stellar material. The binary white dwarfs on the other hand return it all in one explosive, glorious gesture of generosity.
Heavy stars start burning helium early in their lives. As they move across from left to right of the HR diagram they pass the instability strip becoming cepheids, bright beacons that reach out from the far reaches of other galaxies. Gradually as they reach the giant branch of the HR diagram they start burning the fossils left from previous nuclear burning going through increasingly desperate phases of staving off the inevitable as the star tries to increase its internal temperature to resist the increasing gravity at its core. However when the silicon and sulphur in the center starts to burn to produce iron the star has reached the end of the line. Iron can't burn and so just keeps accumulating in the core of the star, as the outer layers keep burning adding to the ash in the middle. The iron core attempts to resist the crushing weight of the outer layers by using the pressure from the electron gas as in white dwarfs. This is possible until the core accumulates enough material to take it over its Chandrashekhar limit. At this point the iron core implodes unable to resist gravity's inexorable pull. The sudden loss of pressure in the underside of the upper layers that was keeping them up causes the entire star to start collapsing in itself. The iron core continues its collapse unto itself until the nuclei of the iron are squeezed together. The electron gas combines with the protons to produce neutral neutrons. These neutrons have the same exclusion property as electrons that causes them to resist being packed together too close. This resistance translates into a outward pressure that can finally resist against the gravity and can halt the collapse of the core. The upper layers which were rushing in following the collapsing core downwards comes up hard against the core as it stops in its collapse. Layer after layer smashes into each other telescoping against the immovable core with its immense resisting power thanks to the neutrons. The incredible heat that builds up produces an incredible explosion that propels the upper layer back out into space, constantly undergoing nuclear fusion and transmutation. All elements heavier than iron is produced in the exploding gas as it is expanding at a tremendous rate. The neutrinos that were produced during the fusing of the electrons and protons follow the exploding gas out. As they overtake the gas a few of them are stopped. The gas get imparted even more energy from these stopped neutrinos forcing them to expand faster. The star lights up in an incredible display of power that is visible from distant galaxies. In fact the energy we see is a fraction of the energy released. Most of the energy goes out with the neutrinos which are hardly stopped by anything. Again in one glorious gesture the star returns all the material that it got from the clouds when it formed and helped build up slowly since its birth back to the inter-stellar gas. Nearly all the material. The core that imploded until it turned itself into neutrons and then stopped, held up by the pressure of the neutrons, survives. This is the neutron star. As the core collapses it preserves its rotation and magnetic field. But the core shrinks an incredible degree, going from the sizes of a star to only 10 kilometers in radius! As a result the neutron star is rotating very fast (several thousand times per second) and is highly magnetized. So strongly magnetized that it can force particles to move only in certain directions. These particles, as they move along the magnetic field, radiate light (radio waves actually). But because of the restrictions on their motion they radiate light in thin beams like the light of a lighthouse beacon. Because the neutron star is also rotating very fast these beacons sweep out the space. If we happen to be in the path of these beacons we detect sudden short pulses of radio waves from a seemingly empty patch of the sky a thousand times a second. This incarnation of a neutron star is called a pulsar (PULSAting Radio source).
Now it is reasonable that neutron stars have the same fate awaiting them as white dwarfs if their mass is increased arbitrarily. The behavior of the neutron gas is the same as that of the electron gas to increased gravitational pull is the same. So as more mass is piled onto the neutron dwarf, it shrinks without getting much hotter, until too much mass is piled onto it. At this point the pressure from the neutrons aren't enough to hold up the star and it must give in to the inward pull of gravity. Then nothing can stop gravity. The star continues its collapse on itself. Its gravity gets increasingly intense increasing its inward pull. Finally the gravity gets so intense that nothing can escape the star anymore, including light. And it becomes a black hole, refusing to release anything even light to the rest of the world. If the blackhole is in a binary system then it will severely distort the companion star's surface, eating up its surface at a furious pace. The material off the companion forms a disk that is very hot and is observable to us using X-ray detectors. However because of their nature, it is impossible to detect blackholes directly and all evidence of their existence is inferred from their presumed gravitational effect on their neighborhood. There are now several excellent candidates for blackholes in our galaxy of roughly the same mass as the Sun.
In actual fact blackholes are expected to radiate like any blackbodies
that possess a finite temperature. This is called Hawking radiation
after Stephen Hawking who was one of the people who helped formulate
the theory of blackholes. But the temperature of a blackhole is very
small only 
degrees celsius above absolute zero (-273.16
degrees celsius), the minimum temperature anything can
have. Consequently Hawking radiation is completely unobservable. Also
it must be kept in mind that the meaning of temperature here is
different from the usual meaning of the degree of random motion of
atoms and molecules in a gas.