Make a budget. Think about how much money you are willing to pay for a computer.
What purpose will it serve. If it is for basic applications like word processing, then look for a cheap model. If you want to play games, you'll need something with a fast processor, lots of RAM, a large hard drive, and good sound and graphics cards.
Where will it be used If you need to take it all over the place, you'll need a laptop. If you intend to leave it in the office or at home on the desk, then buy a desktop.
Who is going to use it? If it's for an office and you have to share it, you might need one with more memory and XP Professional. If you will be the only one using it, and mostly for playing games, then XP Home Edition will serve you well. If however, you are into more videos, creating pictures, and photography, then Vista will be what is what you should buy. Operating systems will be chosen depending on your needs. Remember that a Linux license is free, and there are a lot of excellent and open source applications for it, especially Ubuntu. Right now, the only way to buy Linux desktops is online, but you can buy a Windows computer and then install Linux. Linux also tends to be stabler than Windows, but doing some things will be a pain early on. Fortunately a lot of distributions have excellent help forums, something that you might not get with Windows. If you want to, try both and dual-boot.
Research Scan the Internet, and become more knowledgeable. Compare prices, and whether the computer can be upgraded as needed. Then you are ready to order, either online, or in a Computer Store.

Tips
If you find a computer you like, compare all the prices. You don't want to pay £700 and find the same thing on eBay for £300.
If you're only doing basic things like word processing, see if you can't use a friend's computer, or go to a library.

Warnings
Never pay a lot of money for something unless you are a 100% percent sure you need it.