Buying a domain is easier than you may think, most ISPs provide a simple mechanism for you to register an Internet domain. I am a mamber of Nominet and a Nominet Registrar so I register .co.uk domains direct but in getting to where we I am I have used names.co.uk, 123-reg.co.uk and 1&1 Internet Limited, amongst others. Tip: look at them in the order listed then go back to the first to register your names. It doesn't cost much to register a domain name so don't try to save a few pennies... names.co.uk is going to give you the best service, and I speak from bitter experience.
Internet Domains
In·ter·net - noun a vast computer network linking smaller computer networks worldwide (usually prec. by the). The Internet includes commercial, educational, governmental, and other networks, all of which use the same set of communications protocols.