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It's possible to build a PC for next to nothing these days but it doesn't mean you should. Like others have said before, get a good quality case and power supply. A cheap case will cut you up (Five years ago part of my job was to build PCs as cheaply as possible and I've still got scars on my hands from it) and a cheap power supply will give you instability and can even fry your components. Antec cases and power supplies are popular, reliable, and reasonably priced. For a budget system, Foxconn makes good stuff.
Also stick with brand-name memory. In 486 days, memory was memory, but systems are a lot more sensitive to memory quality now. Kingston and Crucial is good stuff. Un-branded memory is asking for trouble. There are other brands that are good, but Crucial and Kingston are the safe choices.
Try to buy as much of your stuff as possible from one vendor to keep shipping costs down. There's no point paying $15 in extra shipping to save $4 on the price of your video card. I buy most of my stuff from newegg.com and/or mwave.com. My friends and I have been doing business with them for years and their pricing and service are always good.
Aside from that, figure out what you want. You can build a low-end system using an integrated motherboard and literally be done with the work in less than an hour. A more powerful rig with discrete video and sound and network cards will take longer, of course, but it's still not difficult. Anyone who's installed some kind of upgrade in an existing PC ought to be able to build one.