Cosmogony originally referred to the origin of the Solar System, because as you will recall the Universe, or the Cosmos, was infact the solar system, bound by the celestial sphere with the stars. The first idea for the formation of the solar system that is recognizable to modern ideas is that due to Immanuel Kant. Kant was a progressive who argued that revolution was the only way for a society to progress and influenced revolutionaries in United States and France. He continued to be echoed by pre-communists like Saint Simon and civil liberty activists like Frederick Douglass. In philosophy he claimed to have achieved the Copernican revolution. Leibniz and his school of philosophy held that it was possible to answer a philosophical question through pure thought, rational arguments, like geometry, or algebra. Kant insisted that this wasn't possible because mental concepts shaped reality just as much as they were shaped by them. So as the stars acquire a parallactic motion because of Earth's motion about the Sun, the human perceptions of reality are tainted by mental concepts of that very reality. You will recall that Kant had also been among the first to suggest that there may be ``island universes'' outside our own. His vision of the formation of the solar system was simple. A large cloud of dispersed material moved and collided together and eventually objects would form large enough to start collecting smaller particles through gravity. As this happened we would end up with the Sun in the middle and planets rotating around it as the eventual product of these growing particles. From these beginnings of a theory our understanding of the formation of stars and the solar system has come a long way in some ways, and in others not at all. One of the ``problems'' that theories of the origin of solar systems face is the enormous amount of information that we have acquired on the solar system over the years. Any theory that hopes to lay claims on success must explain all these data with satisfaction. This is a considerable challenge to any theory.
The gas that can be observed through absorption lines in stellar spectrum or through emission, (viz., the emission and reflection nebulae) constitute an interstellar medium (ISM) that is divided into separate phases that are in constant dynamic exchange with each other. In the currently accepted model of the ISM, there are three possible phases (states) that the gas exists in. The coldest phase is dominated by neutral hydrogen, at temperatures around 20 degrees Kelvin (-200 degrees Celsius). It is a very tenuous gas, with only about one hydrogen atom every cubic cm. This is a vacuum that is many times better than the best vacuum achievable on earth. This gas fills only about 2.5% of the Galaxy by volume. Warmer than these are the warm clouds, at about 8000 degrees Celsius, constituting of varying ratios of neutral and ionized hydrogen (i.e., hydrogen atom with its electron torn off it). It is even more tenuous than the cold phase with only about 0.05 hydrogen atoms per cubic cm. This phase fills nearly 30% of the Galaxy by volume. Finally is the hottest phase, the hot ionized phase, which is at 50,000 degrees Celsius, and is incredibly tenuous with only 0.0035 hydrogen atoms per cubic cm. Yet it is the most ubiquitous phase which fills about 70% of the Galaxy's interstellar space by volume. Gas from one phase moves into another and they mix as conditions around them change. They also radiate and thus lose energy. the total energy in Galactic system must remain a constant (for the Galaxy to remain stable) and so there must be some source of energy. The dominating sources of energy are the supernovae, which inject huge amounts of energy into the gas that they are exploding into.
Aside from these three phases that are always intimately connected with each other there is another phase of gas that isolates itself from these three phases. This is the molecular gas phase. These are very dense (compared to above three phases) clouds of gas that are cold. They are dominated, as the name suggests, by hydrogen molecule, two hydrogen atoms whose nuclei share their two electrons communally. They vary a lot within this broad characteristics with densities ranging from 100 hydrogen atoms per cubic cm upto nearly a half a billion atoms per cubic cm. They tend to be confined very close to the plane of the Milky Way's disk and show a strong tendency of being concentrated on the spiral arms. They contain substantial amounts of dust. Infact it is believed the dust is instrumental to the forming of molecular hydrogen. The presence of other molecules like CO (carbon mono-oxide) can be observed because of the energy radiated by the CO molecule due to its rotation. This radiation can be detected with radio telescopes and is used to map the distribution of molecular clouds in the sky and to detect the amount of material in them. The molecular clouds constitute nearly half of the galaxy's hydrogen by mass, and yet fill only 0.1% of the Galaxy's interstellar space by volume. They had infact been predicted to exist before they were actually seen. Two astronomers from Princeton, Lyman Spitzer and Martin Schwarzschild realized that the stars in the Galaxy's disc had a random motion (above their overall rotation about the center of the galaxy) that needed some massive objects in the Galaxy that could periodically kick them out of the disk of the Milky way. They postulated that these massive objects were dense clouds of gas, now recognized to be molecular clouds. These clouds are the seats of cloud formation.
Studying molecular clouds using radiation emitted by rotating
molecules through radio telescopes reveal that they are very
fragmented structures. They are comprised of many small globules that
are very dense, upto 
hydrogen atoms per cubic cm. The larger
clouds may extend to 50 parsecs while these small clouds are only half
a parsec in diameter or so. The gravity in these globules tries to
pull the clouds in on itself. The forces that oppose the collapse are
the rotation of the cloud, the heat of the cloud and magnetic field in
the cloud.
To solve this problem of collapse the cloud forms a disk. Around the central object a disk of material forms that is rotating in the direction of the original rotation of the gas cloud. If there is some source of friction in this disk that it will be able to transport rotation outward by speeding up the outer particles and pushing them further out while slowing down the inner particles and pulling them inwards. So in the end a few particles will carry away all the rotation to very large distances while most of the particles in the disk will fall to the center. This allows the central star to grow even in the presence of rotation. Eventually the density and temperature inside the central object is high enough for it to start generating significant energy. This energy first makes its appearance by pushing away material that is trying to fall into the center. Because of the much greater material around it in the disk, it is easier for the proto-star to push out the material above and below the disk, producing bipolar outflows. These outflows are not too hot so they contain small globules of molecular material in them. These globules are called Herbig-Haro objects. Eventually as the proto-star in the middle can start to burn the hydrogen into helium, it generates enough energy to push away the disk around it and turn into a bona-fide star. It stays obscured behind all this dust and gas for some time, during which time it is called a T-Tauri star. These stars have been observed using infra-red detectors.
The birth process puts in constraints on the masses that stars can have. If a star tries to get too heavy then it will start generating a lot of energy very quickly. This will push against the material trying to fall in and will stop them, thus preventing the star from getting too heavy. On the other hand if the star tries to be too small, it will not get hot or dense enough to start burning hydrogen and will be left hardly shining. These very faint stars are called brown dwarfs. Because of their dimness, they are impossible to detect directly, but there are indications that they have been seen through their gravitational effects.
Other than forming a disk there is another way for the collapsing cloud to get rid of its angular momentum. In some cases it can fission into two separate smaller clouds revolving around each other. Most of the rotation is now transferred to the motion of the two clouds in orbit around each other. Each cloud can collapse to form a star resulting in a binary system. It is not clear why a star chooses one of the two possible routes outlined to shed its rotation. But observations appear to indicate that nearly half of stars in the galaxy are binary stars meaning that at least third of the collapsing clouds choose to fragment over forming a disk (because one fission produces two stars).
The origin of the solar system is intimately connected to the formation of the gas disk around the proto-sun as outlined above in the formation of a star. As the gas disk cools the iron and silicates (sand or glass) in the gas condenses out to form dust. The outer parts of the disk is cold enough that ice forms as well, but the proto-star is already releasing enough energy to prevent ice from forming near the center. These iron-silicate dust particles hit each other and coagulate gradually growing in size. As they grow to around 10 km in diameter they are called planetismals. These continue to plow into each other. The bigger planetismals capture and swallow the smaller planetismals they crash into. This soon leads to a run away growth phase, where one large planetismal grows rapidly at the expense of the other smaller planetismals. This results in a planet that has vacuumed up all the nearby planetismals to feed itself. In the mean time the proto-star in the middle starts to generate copious amounts of energy. This energy evacuates the inner disk of all its gas and dust, and the inner planets are left rocky and naked. The outer disk however still has gas which is collected up by the outer planets by gravitational pull. This results in the segregation of the planets into the inner, rocky, small planets and the outer gas giant planets. The lighter material in the inner planets, like oxygen, nitrogen, etc., are belched up from the rocky interior to form the atmosphere, while the heavier elements like iron sinks to the bottom. Heat generated by the crashing of the planetismals onto the growing planet melts the center of the planet and the ``rocky'' planets acquire a molten core which sometimes bursts through in volcanos. Finally when the proto-star starts burning hydrogen it generates enough heat to evacuate the disk of the remaining gas and disk not yet associated with any planet. The left over debris from planet formation in the inner disk are the asteroids, the rocky planetismals. In the outer disk the debris are the comets, planetismals with rock and ice mixed in. As is clear, solar system is likely to form when the star forms a disk around it. In case of binary star formation by the fission of the collapsing cloud there is not expected to be a solar system. So we may expect a solar system in nearly half the stars in the Galaxy.