Although there isn’t any rule that your domain registrar and the host shouldn’t be the same, but you should get the best individually. If you can find a good host someplace and a great domain registrar someplace else, you should stick your guns with it. This also has a security advantage, as if someone gets access to your hosting account, your domain name will still be safe.
Buying from an individual owner is a little different. The official WHOIS domain ownership directory will help you find the seller, then you can work with a domain escrow service to purchase the name. Some registrars also offer escrow services, while sites like Escrow.com and Sedo are geared toward buying, selling, and transferring domain name ownership exclusively. You and the seller will have to determine the terms of the transaction, but carry it out after creating accounts on the escrow site. You can decide beforehand whether the escrow fee is paid by buyer, paid by seller, or split between the two.
Domain names are created to make IP addresses easy to remember. Every computer has an IP address assigned to it - much like a street address. But instead of having to memorize each IP address number, we assign domain names to these numbers so we can easily remember them. The domain name system, or DNS, takes domain names and translates them into their IP addresses so that computers can communicate with one another.