The first thing you should do when you are ready is to select a domain registrar and then open an account with them. Once you have registered you will need to choose your domain name and make sure it is available. The registrar will be able to provide you with your login information so that you may use their interface to edit the name servers and other domain properties.
Your name servers will dictate what web site or server your domain name represents. Your hosting account contains the names of the name servers that you need to point your domain to. Simply log into the control panel of your web hosting account, and you can find your name server information, or just call your hosting company and ask them for it.