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.
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.
GoDaddy — This extremely popular registrar (probably the biggest today) offers .com domain names for $9.99 (plus 20 cents) per year (or $6.99 plus 20 cents if you transfer from another registrar). They have a web interface to manage your domains, free web redirection (where people who visit your domain will get transferred to another web address of your choice), free starter web page, free parked page or free "for sale" page, and an optional private domain registration where your domain is registered in the name of a proxy company. Besides .com, they also sell .us, .biz, .info, .net, .org, .ws, .name, .tv, .co.uk, .me.uk and .org.uk, etc. Note that (as with all registrars) the exact price varies depending on which domain you are registering (for example some domain suffixes are more expensive than others). Both credit card and PayPal payments are accepted.
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.
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.