How did round planets form from the explosion of the Big Bang?

I'm simply going to build on Rahvin's reply since he has been kind enough to flesh out the ground work.I will use decimal point notation to give an indication of the scales, even though it might look messy.Between 0 and 0.0000000000000000000000000000000000000000001 seconds:
We don't have a clue, although String theory hopes to describe this era. General Relativity stops working and we need to take into account quantum effects on gravity (we presume). Probably our notions of time and space, in fact possibly any single notion we have at all does not make sense. Terra Incognita.Between 0.0000000000000000000000000000000000000000001 and 0.00000000000000000000000000000000001 seconds:
There are a few things we do know with some certainty:
There were probably only two forces, gravity and the electronuclear force. The temperature of the universe was about 100,000,000,000,000,000,000,000,000 Kelvin or in shorter words about 100 septillion degrees. The particles that we know today did not really exist, there was no real difference between quarks, neutrinos and electrons yet. What was a single particle back then would manifest itself as two particles now for example. Electric charge didn't exist and neither did the color nuclear charge of quarks.
The observable universe grew from fist sized to melon sized.Between 0.00000000000000000000000000000000001 and 0.0000000000000000000000000000001 seconds:
Here we begin to be more certain. The electronuclear force splits into the strong nuclear force and the electroweak force. Quarks and electrons are now different, although neutrinos and electrons are still the same. We are very sure of this.We suspect that one of the after effects of the forces separating was the result that matter became slightly more common than antimatter.We suspect that at this time the observable universe went from being the size of a melon to billions of light years. We are not exactly certain when in this period the huge jump in size happened or what caused it. We suspect it pumped the universe full of more matter with the energy released by it. Eventually this super expansion (inflation) stops and the universe returns to expanding at normal rates.Between 0.00000000000000000000000000000000001 and 0.000000000001 seconds:
Physics that we properly understand is now in effect. The universe is very large and filled with quarks and electron/neutrinos. The strong force controls the quarks and the electroweak force controls both quarks and electron/neutrinos. The universe continues to expand at normal rates. This is certain.If supersymmetry is true, then at some point in this period it stopped having an obvious effect on the universe. Supersymmetry says that every particle species has a "twin" species with different spin, at some point in this period the universe became too cold for the twins to exist.Between 0.000000000001 and 0.000001 seconds:
From now on things are certain unless otherwise indicated. The physics that we see today starts. The electroweak force separates into the electromagnetic force and the weak nuclear force. Electrons and neutrinos start to exist as separate entities. Electric charge and electric current as we know it begin to exist and also light comes into existence. The universe is basically a very hot soup of these particles.Between 0.000001 seconds and 1 second:
Finally the universe is cold enough to allow quarks to combine into protons and neutrons and other hadrons (name for particles made of quarks), taking us one step closer to having atoms. The universe is now made of hadrons, electrons, neutrinos, anti-hadrons, anti-electrons and anti-neutrinos.
Eventually it is too cold for new hadrons and anti-hadrons to be created, at this point production of these particles effectively ceases. Hadrons and anti-hadrons now begin annihilating each other until there are basically no anti-hadrons left and only a few hadrons. The surviving hadrons are a miniscule fraction of the original amount, but they will form the whole universe we see today.
Electrons, neutrinos, anti-electrons and anti-neutrinos now vastly out number hadrons.1 second to 376,000 years:
In the next few seconds the universe becomes too cold for new electrons, neutrinos, anti-electrons and anti-neutrinos to be created. Just like the hadrons, they begin to annihilate. Leaving only a tiny bit of the original amount. Essentially no new matter will be created again.
The temperature continues to drop, until it is cold enough for protons and neutrons to stick together forming atomic nuclei. This continues until the universe is 16-17 minutes old, when the temperature drops beneath millions of degrees. This creates mostly hydrogen and helium nuclei.
The universe is now made mostly of light trapped between the hydrogen and helium nuclei and the electrons and stays that way for thousands of years.
At around 70,000 years the universe stops being just a big soup and starts to become clumpy. Irregularities start to develop. Dark Matter probably causes the irregularities to develop, until the universe goes from being a soup to being a bunch of lumps separated by emptiness. This is the first point at which Dark Matter is noticeable.376,000 years to 150 million years:
The universe becomes cold enough for the hydrogen and helium nuclei to capture the electrons, creating hydrogen and helium atoms. Matter is now electrically neutral and light escapes and begins to move freely. However nothing makes light, so after this initial burst at 376,000 years the universe becomes dark.150 million to 1 billion years:
Isolated energetic objects begin to exist. That is objects which are hot, independent of the background temperature of the universe. The first big black holes form, sucking in the surrounding matter and blasting out jets of radiation. These huge black holes together with their accretion disks (the spiral of matter surrounding them) are called quasars. The first stars begin to form, outside of galaxies. Eventually the quasars will settle down to become galaxies. The earliest stars produce the heavier elements in their interiors, adding something other than hydrogen and helium to the universe.The galaxies begin arranging themselves into groups through complex gravitational interactions. On larger scales the groups assemble into clusters. The clusters into superclusters. Finally superclusters string together to form filaments.1 billion years to 8.5 billion years:
New generations of stars are produced in galaxies.I could go on from here to our galaxies formation and then our solar system, but I don't want to be "Earth-centric". At this point the present day structure of the universe has developed, except one more event occurs.8.5 billion to 9 billion years:
The universe starts to expand faster again, although not at the speeds as the early super expansion (inflation). It begins to expand faster and faster as time passes and continues to today. It is suspected that a new form of energy, dark energy, is responsible.Edited by Son Goku, : Change for clarity.

Hey slevesque,Actually as a physicist I usually use the phrase "our universe" or even "the universe" for the observable universe. The actual entire universe is usually called spacetime or the "present hypersurface". This is confusing on my part though, so I've changed the post to be less confusing, using observable universe instead. Well, there is nothing to say that the universe is definitely infinite. Recent WMAP measurements show that space is essentially flat (Euclidean). However this is just consistent with it being infinite, we'd need something more solid to make the conclusion of it being infinite more solid.

Hey Huntard,In the Big Bang model, if the universe is infinitely large now it was infinitely large in the past. The expansion means that any "piece of space" that was some size 10^(-36) seconds after the Big Bang, is now vastly larger. General Relativity breaks down at this point. The infinitesimally small singularity is an artefact of General Relativity being no longer applicable. In truth we can trust General Relativity up to a certain point in time, at which point it says that any given region of the universe today was extremely small. Going beyond this, back to the time when General Relativity predicts everything being infinitely small, is trusting the model beyond its own limits.An analogy can be found in some models of ice. There are statistical mechanical models of ice, that describe ice very well up to about 0 degrees. The models predict that ice becomes more and more brittle as you increase the temperature. However they predict that ice becomes infinitely brittle at 0 degrees. Of course this is incorrect, what really happens is that ice becomes water at 0 degrees.
Just like General Relativity the model works perfectly fine up until it develops a singularity (in this case infinite brittleness), to go further you need to add new details. In the case of the ice models, you need to make the model less simplistic and add more properties of water to it. In the case of General Relativity, we don't know.