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.

Domains are nonmaterial goods. When sold, the only transaction taking place is transfer of domain rights from one user to another. Barring any form of copyright or trademark violation, virtually any domain name can be bought or sold. Generic domain names, such as car.com or computer.com, are not legally protected and can therefore theoretically be reserved by anyone.
Domain name registrars, in case you didn't know, are the companies that manage all the website domain names you'll see (EG: Inc.com) - the fingerprint of your business, which may also include the hosting and privacy measures. For example, by default many companies will actually over-price the simple process of keeping your registration information private (which if it isn't can be found via a simple Whois search).
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.
New domain registrations can be added to a new or existing Netfirms account. Each Netfirms account includes 1 free e-mail account (unless you upgrade to a hosting package). If you are looking to register multiple domains and want an e-mail account for each, you can either create a separate Netfirms account for each domain or upgrade a single Netfirms account to a hosting package.
Is your domain name portable if you change service providers? I’m starting a non-profit and I want to hold the name, but eventually I will fire someone to do the website development and want them to be able to use the platform they think they can work most effectively in. If I were to register with GoDaddy for services and get a free domain name… do I lose it if I switch to another web-hosting provider?

A handful of domains will have restrictions on them, which means you can only purchase them if you meet certain criteria or have authorization (some examples are .gov, .edu. and .mil). But most extensions are available to everyone. In fact, most country code Top Level Domains (ccTLDs) are available for anyone to purchase, even if you don’t reside in the country in question.
1&1 makes buying your domain name simple. The more complicated part is on your end in figuring out what you want your domain to be named. Once you have figured out what you want your domain name to be, 1&1 helps you with the rest. When you purchase a domain with 1&1, the cost is inclusive all the registration fees and affiliated E-Mail accounts with 2 GB storage space. Choose a domain package you need, and the registration is free. It includes sub-domains, a control panel, E-Mail account and support. Furthermore you use the website builder provided to you by 1&1 to construct your own website around your new domain.
In the first quarter of 2015, 294 million domain names had been registered.[17] A large fraction of them are in the com TLD, which as of December 21, 2014, had 115.6 million domain names,[18] including 11.9 million online business and e-commerce sites, 4.3 million entertainment sites, 3.1 million finance related sites, and 1.8 million sports sites.[19] As of July 2012 the com TLD had more registrations than all of the ccTLDs combined.[20]
ICANN publishes the complete list of TLD registries and domain name registrars. Registrant information associated with domain names is maintained in an online database accessible with the WHOIS protocol. For most of the 250 country code top-level domains (ccTLDs), the domain registries maintain the WHOIS (Registrant, name servers, expiration dates, etc.) information.
Name servers. Most registrars provide two or more name servers as part of the registration service. However, a registrant may specify its own authoritative name servers to host a domain's resource records. The registrar's policies govern the number of servers and the type of server information required. Some providers require a hostname and the corresponding IP address or just the hostname, which must be resolvable either in the new domain, or exist elsewhere. Based on traditional requirements (RFC 1034), typically a minimum of two servers is required.
A fully qualified domain name (FQDN) is a domain name that is completely specified with all labels in the hierarchy of the DNS, having no parts omitted. Labels in the Domain Name System are case-insensitive, and may therefore be written in any desired capitalization method, but most commonly domain names are written in lowercase in technical contexts.[2]