Typically domain registration is paid yearly, or multi-yearly, if you so decide. The price is about $11, though you'll might be able to find it cheaper at some registrars, especially if you find a coupon to use. Prices also vary depending on the type of domain you have in mind. I'm mostly familiar with .com, .net and .org.
Personally, I use Namecheap for domain registration, and a different company for my web hosting needs.