If you are signing up with a hosting provider, most of the time you can just choose your domain name right there at sign up.

If you want to just buy a domain name for now, you can easily "point" it to a hosting provider (where you would actually put a website) later.

To do so, you just have to go to a domain name registrar and purchase it. There are countless numbers of them, but some of the more well known ones are GoDaddy and Namecheap.

The registrar will let you know on sign up if your domain name is already taken. Keep the username and password you choose on sign up handy so you can change the name servers later to point them to your web hosting provider.

To do this, read how to keep your domain name.