There are numerous domain name registrars. Listed below are just a few, along with my comments, if I know anything about them. Note that the domain name industry is highly competitive, with prices wildly fluctuating throughout the year, every year, so it's impossible to really mention accurate prices below unless I spend all my time updating this page. Please check their sites for the latest rates. All prices below are in US dollars.
Next, someone has to tell the rest of the Internet that google.com points to 126.96.36.199. This is done by a “registry”, which is also the wholeseller that provides domains to registrars. Each top-level domain (TLD) — .com, .net., .org etc — has a registry that manages it. The .com TLD has been managed by the same registry since the beginning of time — an extremely profitable monopoly called Verisign. More on that later.
Many registrars reserve the right to revoke your domain name for specific reasons, typically if you use the domain for illegal purposes or purposes deemed unacceptable (such as spamming). Many contracts contain a clause letting the registrar delete your domain name for no apparent reason. The implication, of course, is that the domain name is the registrar's, not yours.
Namecheap is a solid choice for registering your domain name. Plus, their site is incredibly intuitive and easy to use, especially on their domain management pages, which can be incredibly helpful. They offer reasonable priced domains, and have a free DNS service, and WHOIS protection. They also offer SSL encryption, for those looking to beef up the security of their domains.
Getting a domain name involves registering the name you want with an organisation called ICANN through a domain name registrar. For example, if you choose a name like "example.com", you will have to go to a registrar, pay a registration fee that costs around US$10 to US$35 for that name. That will give you the right to the name for a year, and you will have to renew it annually for (usually) the same amount per annum.
What’s easy to forget, though, is that Verisign have managed .com for the past 20 years without so much as a hiccup of disruption or downtime, and that there’s no guarantee that a more democratic or competitive process would have resulted in the 2 decades of .com stability that we’ve enjoyed. Internet governance is obviously important, but we should remember that the overwhelming majority of users don’t know or care what’s going on behind the scenes.