Domain name registrations are priced on a subscription-like model that allows a person or business to register that domain name for a certain period of time (usually in annual increments). At the end of the registration period, you (the domain name registrant) have the option to renew the domain name registration for an additional period of time, or let it expire. It is important to renew your domain name registration, or you may find that all of your work building traffic and views to your site ends up benefiting someone else (in the instance that someone else registers your domain name after you let your registration expire), and potentially costing you more in rebranding.
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 have a web site, you should seriously consider registering your own domain name. A domain name is a name like "thesitewizard.com" or "thefreecountry.com", which you can use to refer to your website. Note that you do not have to be a company or organisation ("organization" if you use a different variant of English) to register a domain name. Any individual can do it too.
The hierarchy of domains descends from the right to the left label in the name; each label to the left specifies a subdivision, or subdomain of the domain to the right. For example: the label example specifies a node example.com as a subdomain of the com domain, and www is a label to create www.example.com, a subdomain of example.com. Each label may contain from 1 to 63 octets. The empty label is reserved for the root node and when fully qualified is expressed as the empty label terminated by a dot. The full domain name may not exceed a total length of 253 ASCII characters in its textual representation. Thus, when using a single character per label, the limit is 127 levels: 127 characters plus 126 dots have a total length of 253. In practice, some domain registries may have shorter limits.
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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.