First, research. Before you start buying anything, learn as much as you can about computers. Then, you'll be ready to start looking at...
CPU - This should be the easiest to decide on. There's really only 2 choices, Intel P4 or Athlon 64 socket 939. Most people would pick Athlon. Then just pick the model that fits your budget.
Motherboard - another very easy decision. After you've decided your CPU, pick out the motherboard that fits the socket. If you've picked an Athlon 64 socket 939 CPU, there are again really only about 5 choices.
Hard drive - quick and easy. Probably want to stick with SATA on a mainstream budget, Raptor on a higher budget, Raptors in RAID for high-end system. Basically pick out what fits your budget.
Video card - takes some time, but also very dependent on your budget. Two choices, ATI or nVidia, model is chosen to budget.
RAM - four major brands, OCZ, Corsair, Crucial, Mushkin. Most people would use 1gb. The FSB and version you get of the ram is dependent on what you plan to do with your system. Overclock? Get high-end model (such as the OCZ EL Platinum Revision 2, or the Corsair XMS), maybe a higher FSB (such as DDR466 or DDR500 as opposed to the regular DDR400). If you don't overclock, DDR400 Value ram is fine.
Power Supply - not very hard choice, but make sure you get the right brand. OCZ, Enermax, Antec, Tagan, Fortron, PCP&C to name a few. Many people are confused between the high-watt-low-price and the -low-watt-high-price power supplies, and end up buying the former. You want GOOD brand, med-wattage, but most importantly, GOOD BRAND.
Drives - Probably want DVD-/+RW on the top, CD-RW or DVDR on the bottom. Get brand name drives and you're set.
CPU Cooler - only if you'll be overclocking. If not, just stick with the stock heat sink/fan that you get with the retail package of your CPU.
Case, mods, and lighting - last thing. Takes forever to choose, a good brand name case would probably fit you best but low-names are ok. It should have the features you want (size, weight, cooling, form factor, placement of slots etc), and most importantly, you like it.
Everything else is pretty much optional, such as mouse and keyboard, sound card if you want one, speakers, monitor, etc etc. Just get a good brand of each, make sure you get what you want (right speaker setup (2.0, 2.1, 5.1, 7.1, etc)), and you'll be fine. There are only a few of each that people would get. I suggest Logitech MX510 for mouse, any keyboard is fine, Soundblaster Audigy2 ZS for sound card, Logitech MX530 5.1 speakers, a good brand of 19" CRT monitor.
Pricing - (gaming computer) CPU/Motherboard should take up about a quarter of your budget. Video card should take up about a third of your budget. RAM, hard drives, optical drives, PSU, everything else should only take up a third. Peripherals should take up another quarter if you need em. If not, spend it on video card. My math may not add up but basically:
Video card - top priority. Should be the most expensive thing you buy.
CPU/Motherboard - important, but these usually don't cost too much.
RAM - only expensive if you overclock.
Optical drives - you want good ones but generally are pretty cheap.
Hard drives - shouldn't cost too much if you use SATA, if you use Raptors in RAID these can get pretty damn expensive. RAID isn't worth it IMO unless you have lots and lots of floating money.
Peripherals - you want good ones but generally are pretty cheap.
Sound card - there is only one. Soundblaster Audigy2 ZS. 80 bucks.
Ok, good luck! Some people may disagree with my post, but this is solely based off of my experience and what I have read. Remember, building a computer isn't to reduce cost, custom builts usually cost more. These are usually only for learning purposes and something to brag about once you have the ultimate system. But most of all, have fun!!
And make sure you reseach a lot before you buy. Rule of thumb.
EDIT: Sorry if I wrote a book. I was actually first to read and first to post, but it took me forever to write this thing, so I may be a little behind. 🙂