I personally have used godaddy.com in the past. They were fast, efficient, and I never had any problems. The only interaction I had with them is to sign-up and to change my DNS addresses so that my host and my site could be linked.
It's really an easy process but if you do need help, you can google "domain purchase tutorial" and I'm sure you'll find some out there that give you step-by-step walkthrough of buying a domain.