Many online shops have the number 24 in them, to signify 24 hours a day – you may also be able to integrate numbers into your domain in a meaningful way to make them unique. Be careful though, because many cultures attach a lot of significance to certain numbers. Make sure that your number doesn't represent bad luck or other negative things in the country you're operating in.
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.
A domain name registration is simply reserving your website's name for a specified period of time. The two parties involved with a domain registration are generally the user who is registering the domain and the domain registrar. The domain registrant is the user who actually registers the domain name and the domain registrar is the company who helps that user with their domain registration.
Note that you can also transfer your domain name from one registration service to another. You'll want to do this if you're not satisfied with your current domain hosting service, if you find a better deal when your current registration is coming due, or, most likely, if you've signed up with a web hosting service that will also transfer your name to its site. Expect to get the transfer for free, but if that isn't offered, search for another domain hosting service.
Who is in charge of all of these processes? Most countries manage a Network Information Center (NIC). An NIC is the main database that has all the information regarding what domain names have been registered and the IP address associated with each of those domains. The nonprofit organization the Internet Corporation for Assigned Names and Numbers (ICANN) is in charge of creating and managing the procedures for internet namespaces.
Domain names used in works of fiction have often been registered in the DNS, either by their creators or by cybersquatters attempting to profit from it. This phenomenon prompted NBC to purchase the domain name Hornymanatee.com after talk-show host Conan O'Brien spoke the name while ad-libbing on his show. O'Brien subsequently created a website based on the concept and used it as a running gag on the show.
In order to register any domain, you must provide certain personal information that you may not wish to be publically searchable in the Whois database. Signing up for WhoisGuard is a great way to keep your registration data private. WhoisGuard acts as a "shield" for your searchable information, displaying the address, phone number, and email of the domain registrar (Namecheap, e.g.) instead of your own. Keep in mind that WhoisGuard is an optional security add-on that must be renewed separately when you renew your domain.