Namecheap — This company provides .com domains for $10.69 (plus 18 cents) per year ($9.69 if you transfer from other registrars). Along with your domain, you get free email forwarding, free web redirection (where anyone going to your domain is automatically directed to another address of your choice), free domain name parking, etc. For the first year (or at least, at the time I checked their prices), you can also have their WhoisGuard (where your particulars are masked from public view) for free. They have a wide variety of domain name extensions available, including .net, .org, .biz, .info, .us, .co.uk, .co, .de, etc. You can use either a credit card or PayPal for your purchases.
If you’re still with me then you might be wondering who came up with all of this. The answer is ICANN — the Internet Corporation for Assigned Names and Numbers. ICANN is a non-profit whose role is to coordinate all the names and numbers that keep the Internet online. They outsource a lot of the heavy domain name lifting to registries like Verisign, who pay ICANN for the privilege.
When you type google.com into your browser, the domain is split into parts by the “dot”, from right to left. The first part is “com”, so your computer checks the root zone file to see which registry manages the .com TLD. It then checks with this registry to see where the next part, “google”, points to. The registry returns the IP address 220.127.116.11, and your computer can then ask Google to send their homepage over.
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.
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.