Keep in mind, however, that free domain names are usually free only for one or two years, after which the registrar will bill you for the annual or biennial fee. In other words, the provider of the free domain name pays only for the first billing from the registrar. Also take note of whether or not the provider charges a fee for setting up a domain name. Most services offer to transfer an existing domain name to their servers at no cost, but sometimes you'll find a setup fee over and above the registrar's fee.
A domain name consists of one or more labels, each of which is formed from the set of ASCII letters, digits, and hyphens (a-z, A-Z, 0-9, -), but not starting or ending with a hyphen. The labels are case-insensitive; for example, 'label' is equivalent to 'Label' or 'LABEL'. In the textual representation of a domain name, the labels are separated by a full stop (period).
If you already have a web host, obtain from them the names of their primary and secondary nameservers. Don't worry if you don't understand what these things mean. Just save the information somewhere. The information can usually be obtained from their FAQs or other documentation on their site, usually under a category like "domain name" or "DNS" or "domain name transfer" and the like. If you can't find it, email them. You'll need the information to point your domain name to your website after you buy your domain. Having said that, if you don't have a web host yet, don't worry. Just read on.
My personal preference is to register the name directly with a domain name registrar rather than through my web host. I've heard stories, in the past, of less-than-reputable web hosts that registered the domain under their own name, making them the owner of the domain rather than you (although I don't know if such web hosts still exist today). Registering direct with a domain name registrar allows me to make sure that I am registered as the owner, the administrative and technical contacts. Being the owner is vital — if someone else places himself as the owner (such as your web host), he can always decide to charge you some exorbitant fee for the use of the name later, and there is little you can do. The various other contacts are less vital, but may still play important roles, depending on your registrar. For example, for some registrars, the administrative contact's approval is required before a domain name is transferred out of a web host (or at least, it used to be). If he/she cannot be contacted, the technical contact is used.
A great domain name is a concise, easy to type, and memorable URL that reflects your brand or your website’s subject matter. Avoid using hyphens, strings of numbers, or unnecessary words to make it easy for your visitors to remember and find your website. Remember: A great domain name is one that your visitors can type correctly on their first try.