As is typical of "Answers in Genesis" they don't seem to even have a basic understanding of what they are talking about. They are confusing how gases normally behave in common experience (i.e. on scales of human experience). When dealing with a nebula, we are talking structures that expand for light years in all directions... Read that again: light year*s*! Over such great distances, even the most diffuse material will have enormous gravitational attraction. Because there is a whole lot of mass there (for instance, the Orion Nebula has a mass over 2000 times that of our sun). For the sake of your sanity, as soon as someone uses Answers in Genesis or Conservapedia as a source, just walk away. They are notoriously biased.
As for the process itself, and to explain it properly, one must first admit that there are still many questions that are not yet answered. However, we still have a fairly good idea how it works (and not knowing parts of how something happened does in no way invalidate a sound theory). Harvard takes a rather humerous and simple approach in explaining it:
Steps to the formation of stars and planets:
1 Clouds of gas form within galaxies.
2 Formation of structure within the gas clouds, due to "turbulence" and activity of new stars.
3 Random turbulent processes lead to regions dense enough to collapse under their own weight, in spite of a hostile environment.
4 As blob collapses, a disk forms, with growing "protostar" at the center.
5 At the same time, bipolar outflows from forming star/disk system begin.
6 Material is processed, moving in from the blob to the disk. What is not lost in the outflow builds up on the protostar.
7 When the protostar begins to undergo fusion, it becomes a real star.
8 Once the outflow ceases and the "accretion" phase that lead to the buildup of the star ends, a disk of "leftover" material is left around the star.
9 At or near the end of the star-formation process, the remaining material in the "circumstellar disk" (a.k.a. "protoplanetary disk") forms a variety of planets.
10 Eventually, all that is left behind is a new star, perhaps some planets, and a disk of left-over ground-up solids, visible as a "Debris Disk" around stars other than the Sun, and known as the "Zodaical Dust Disk" around the Sun.
The National Radio Astronomy Observatory has a great article about actually observing some of the early stages involved in star formation. Again, while not everything is understood, they are gathering more clues.
Stars are formed, astronomers think, when such a cloud of gas and dust collapses gravitationally, first into clumps, then into dense cores, each of which can then begin to further collapse and form a young star. The details of how this happens are not well understood. One difficulty is that most regions where this process is underway already have formed stars nearby. Those stars affect subsequent nearby star formation through their stellar winds and shock waves when they explode as supernovae.
The astronomy department at the University of Arizona has a web page (horrible design in my opinion, but good info) that also goes into a lot of detail on the things we do know, the things we hypothesize, and the things we don't know at all. Interestingly, the University of Illinois also has a page that covers the subject, albeit with a different focus on what they consider important. However, they all agree that gravity does a great deal of work. As a matter of fact, it's easy to find pages from pretty much any accredited university out there (University of Oregon) that discusses the same subject matter. Now, one may say this is an argument from authority, but keep in mind that this is a competent authority with expertise in the subject. Much like one wouldn't ask a brain surgeon to be a car mechanic, it's probably best to leave astronomy to actual astronomers.