Computers are getting cheaper - but so are computer parts. You can often save money by assembling one yourself to suit your own needs, and it doesn't have to look like Frankenstein's monster. It's also a great way to learn more about how computers actually work - although remember you'll have less customer support if things go wrong.
If in doubt, always make sure your system has plenty of hard drive space and RAM, as well as connection sockets - these will all help you avoid needing another new machine too soon!
Motherboard
This is where the actual processing gets done. There are different types available, with either AMD or Intel processors. The motherboard also houses slots for memory, and boards for extras such as video and sound, and a modem for dial-up internet access.
Power supply (PSU)
You'll need the right kind of PSU to avoid frying your motherboard. (Always handle chips with care - static can destroy them, so use an anti-static wrist strap or earth yourself properly.)
Memory
RAM (Random Access Memory - check out a glossary if the jargon gets too much) is crucial. If you want to run a lot of applications, it's RAM you need. There are two kinds, DIMMs and SIMMs, with newer motherboards needing the former. Pick a motherboard with plenty of memory slots so you can always upgrade in the future. You're best off with at least 512 Mb to start with.
Hard drive
People often refer to this as the main bit of the computer, but actually it's the permanent memory rather than the "thinking" part (which is the CPU). Hard drives are measured in gigabytes - you could store the complete works of Shakespeare and much more besides in well under 1 Gb, but many modern applications need plenty of hard drive memory space. You'll probably want at least 40 Gb - more if you intend to store a lot of pictures, music or video.
Input and output
There's an almost endless array of extras for a PC, but any modern system will want a CD drive at the least, ideally a DVD drive. An "-R" suffix means it will record as well as read data, and "-RW" means reads, writes and rewrites. So if you want to burn your own discs, make sure you've got either of these. For general use, the video and sound cards on your motherboard may suffice - but you'll need extra, more powerful ones if you play games or do high-end graphics work. Finally, you will want plenty of USB ports (for printers, scanners or Internet connections) - also consider Firewire for further connectivity. If you want to connect to other PCs or a broadband network, you'll need a network card.
Putting it all together
Once you've got all the compatible bits, you need a case - make sure it's big enough for the motherboard. As for instructions about connecting everything up, there are useful tutorials at www.buildyourown.org.uk and BuildPC. There are also plenty of books on the subject. Good luck!