One thing that hasn't really been covered well enough above: How to choose the components you're going to be throwing into your computer. For tips on actually getting this stuff once you've decided what you need, check out How to buy computer parts.
For the purposes of this node, I'm going to assume you're making yourself a system you're going to use to play games and for the internet.
Disclaimer: For all you know, I don't know what the fuck I'm talking about. Keep this in mind whenever you're basing purchasing decisions on what people on the internet tell you.
You need a case to put all this stuff in. You're going to want an ATX case. I don't really know what that means, but it's quite likely if you don't get one that your motherboard won't fit in there. That'd be bad.
I suggest that you do not skimp on the case. If this is your first time building a computer, you are going to want to have enough room to work in there. Not being able to see what the hell you're doing is a bad thing, as is not being able to fit your hand where it needs to go.
If you use a lot of peripherals that use USB plugs, try to get a case that has built in slots to plug them to. Less mucking about in the back of the b0xen.
If you have a fair amount of cash to blow, get a nice Aluminum case from Lian Li. Hell, even if the rest of the components are crap, at least it'll look cool.
Also with the case, you're going to need a power supply. These are usually included. Most places suggest getting a 300 Watt power supply or more. I'm not going to argue.
The next thing you're going to need to decide on is your processor. This is important stuff and such. Basically, now-a-days, you're probably going to go with one of two choices, a Intel Pentium 4, or an AMD Athlon XP. Or, now the AMD Opterons are looking rather nice, all 64 bit technology and all. I'd only go for something cheaper if you're really on a budget, as you want to be looking at not only handling stuff out now, but in the future as well.
In general, it seems to be a good idea to buy 6 months behind the technology. At that point stuff is still pretty close to top of the line, but you can get it for a good value.
I suggest purchasing an AMD made processor, as most people agree that you're getting more bang for your buck with them. The majority of Intel's sales seem to be based upon brand name recognition, as opposed to providing a better product. This may work for most computer users, but we're Geeks, people. You must be by definition if you're building your own computer. And you want to be getting the best product you can for what you're willing to pay.
Anyhow, I got myself an Athlon XP 1800+ processor. I think they had dropped the price down a week before I got mine. I paid $159CND, which isn't bad for a damned fine piece of Engineering. Of course, by the time you read this, it'll probably be outdated. Like I said, buy 6 months behind the technology and you should be ok.
Update: Of course, by now this particular processor would be horribly outdated. I wrote this writeup in 2002. Now, in 2005, you expect a hell of a lot faster than 1800+ in a cheap ass laptop. So, if any of my guidelines are to work, scale them appropriately. I still believe my advise to buy 6 months behind the technology is valid, for getting good deals.
Once you know what kind of processor you want, you need to decide on the motherboard. The most important part is making sure that your processor will actually FIT.
Athlon and Duron (Athlon's predecessor) processors use motherboards with a Socket A, Pentium 4's use a Socket 478. Apparently the Opterons use a 939 pin socket. Anyways, just make sure your processor will fit before you buy the board.
The next thing to think about is your RAM. I suggest purchasing a motherboard that can handle the coolest new type of RAM on the market. You want to be thinking about upgradability. I mean, if you bought something that took SDRAM back when SDRAM just came out, you're fine for now. However, if you had skimped and gotten whatever was out before that, well, you're probably SOL.
So, at the moment, you want a motherboard that takes DDR RAM. It's fun, and still nice n' cheap. Memory is usually fairly cheap. I suggest getting at least a 512 meg stick of it.
Next you want to look at what kind of slots you want. Unless you're only going to be using it for word processing, you want to have one 4x AGP slot, to stick a fancy video card into. More on that later.
You're also going to have a number of PCI slots. You probably want at least 4. 5 is good. Go for five. Once again, you're looking at upgradability issues here.
One of the things that would go in one of those PCI slots is a sound card. However, a lot of motherboards come with a sound card built into them. These used to be crappy, but now they're pretty good. The determining factor in if you should use one of these is your speakers. There's no use in getting a neat-o sound card if you're using shitty speakers.
If you get a motherboard with built in sound, and later decide to upgrade, it's fairly simple to disable the motherboard's sound card and use yours.
Some will also come with a built in video card and/or Ethernet card. I suggest against getting one of these. You don't want to be stuck with the built in stuff.
Around this time, you might also be looking into having onboard SCSI connectors. Personally, I wouldn't bother. If you got the extra cash, go ahead, but I'm a starving student, so I didn't really look into SCSI all that much.
Anyhow, once you know what you want, it's time to choose which brand to buy. Again, I suggest not skimping too much on this step. You're saving money by building it yourself, you might as well get good components. I myself got an ASUS A7S333.
Ok, you've got yourself a motherboard, case, processor, and some RAM. You need a video card, young Skywalker. There is no reason not to get one with at least 64megs of video memory. This is what I did, since I was going to be skimping on the monitor anyways. If you're getting/have a nice monitor and want to run all the funky new 3D games, it might be a good idea to spring for better. But, as fuzzie claimed in the catbox, for the vast majority of applications, you won't notice the difference between a $100 card and a $4001 one.
Update: Again, now a days, a 64 meg video card is on the lower end of the scale. Adjust accordingly.
Floppy Drive: Doesn't matter. How often do you really use it since high speed internet came around? I personally pulled one out of the old junk computer that had been sitting in the closet for 7 years.
CD-ROM: You're going to want a CD-R. You quite likely want a DVD-ROM, and maybe even a DVD Burner. You may also want a plain CD-ROM drive, to ease wear and tear on the CD-R drive. Making your own CDs is fun. It's up to you, I personally picked up a cheap Panasonic 24x CD-R drive OEM. Couldn't find any drivers for it specifically, but the generic drivers worked just fine.
Oh yeah, having a hard drive helps. Adequate storage space is good. Remember, Windows XP takes up like 1.75 Gigs or so. Depending on what you're doing with it, you may want nice and quick access times. In which case you're looking at SCSI drives. That'll eat up one of your PCI slots, unless you bought a motherboard that had built in SCSI adaptors. Most of us, however, will do fine with just plain IDE connections.
Higher RPM rates will make search times lower, and apparently the faster drives also last longer. Or at least N-Wing says so, that personally seems rather counter intuitive to myself. But, he knows a load more about computers than myself. But storage is the main issue here. I don't suggest getting less than 100 gigabytes of storage space now-a-days. This is a step up from the 40 gigs I have on the computer I built first writing this writeup, which was a step up from the 6 on the old family computer.
You probably want to be hooked up to the Internet, where you can look up cool info like this. If you are getting some kind of a dialup service, you need a modem. If you're getting a cable or DSL connection, the modem will be external, and you will need to hook it up to an Ethernet card. Fortunately, both of these are fairly cheap. Each will take up one of your PCI slots.
Ok. Case, Power Source, Processor, Motherboard, RAM, Sound Card (Maybe), Video Card, Floppy Drive, CD-R, Hard Drive, Ethernet Card. Throw it all together as described above.
The only thing I would like to add about the actual assembly process is a bit of a warning. When you get the case, the spots for the PCI cards and such may have a little metal thing that you will need to push out. Be careful with that. It can be sharp. Use a pen or something. I shaved a good millimetre of skin off my index finger, and I can still see the scar on the knuckle.
You might want to install some sort of an operating system at this point. Which one?
I'm not going to touch that subject with a 10-foot pole.
I like to think I'm not that stupid.
1: All cash amounts in Canadian dollars.