The disk-shaped nebula around a young star contains all of the raw materials -- gas and dust -- which can eventually accumulate into planets.  How this matter actuallly ends up in planetary form is still a matter of debate.  Our observational technology is not good enough yet to allow us to directly view a planet accreting out of the primordial cloud.  Thus our best explanations for planet formation are driven by the work of theorists, who use the known laws of physics and computer simulations, to derive possible models.

The first of these models has a history that traces back to Immanuel Kant and Pierre-Simon Laplace, and is commonly refered to as the nebular hypothesis.  However here I'm calling it by the more descriptive slow and steady: planets cobble together slowly, starting from microscopic dust grains which grow into hierarchically larger and larger building blocks.

As they orbit around their parent star, grains collide and stick, growing into pebbles.

These pebbles can aggregate into gravel, then rocks, then boulders, and so on, until you get to planetesimals kilometers, and then hundreds of kilometers across.  There is still considerable debate about the details of the various steps in this process -- imagine collisions between rocks with such ferocity that they are more likely to disintegrate them into smithereens than they are likely to stick together.

And for planetesimals many kilometers across, gravity between these growing masses become important.  Instead of their motions being dominated by the gravity of the central star dominating (which keeps all of the material in the disk in orbit about the star), planetesimals grow large enough that they begin to be drawn to each other.  This can lead to a massive proto-interplanetary game of billiards with massive rocks colliding with each other, debris scattering, and then drawn back in by the gravity of the dominant masses.

Over time, the most largest of the rocky cores become massive enough that they pick up the gas in the protoplanetary nebula.  (The make-up of this nebula is the same as that of the parent star: roughly 75% hydrogen and 25% helium by mass, and a few percent for all of the other elements in the periodic table.)  The most massive cores become even more massive as they accrete the abundant gas.  This makes them accrete even faster, which eventually leads to a feedback loop resulting in runaway accretion.  The new gas giant planet sweeps up most of the matter in its immediate vicinity.

Based on computer simulations, this process for building planets can take tens to hundreds of millions of years, and hence the "slow and steady" moniker from earlier.

A completely different process was proposed in 1997 by astronomer Alan Boss at the Carnegie Institution in Washington DC.  For a protoplanetary disk that started out with sufficient mass, it is possible for for part of the disk to become unstable:  Through random motions some of the gas pools together at a point in the disk, which increases the gravitational attraction of that location.  More gas gets drawn in, and this leads to a runaway effect again.  A "gravitationally instability" grows, and without seeding by a accreting solid core like in the first planet building technique, the gas collapses quickly into a gas giant.  This can happen in a million years, which may seem long by our standards but is relatively quick on a solar system timescale.

Since Boss first announced his idea, there has been theoretical modeling that has been done by him and others.  There is also continued debate about the details of both of these techniques for explaining planet formation.

[TO BE CONTINUED ...]