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.
GoDaddy used to be a place I'd recommend only as a joke, but has significantly improved their service. They'll recommend you domains based on certain keywords, which is useful if you've not got the one you want available (they'll actually remove these from the search to try and not break your heart), and they've also significantly improved their hosting offering. They still continue to offer weird things like "email services" that other hosting companies provide too.  Our GoDaddy Review.
If you are looking for a TLD other than those listed above, our DNS services support domains in almost every TLD, as long as the registry and your registrar will delegate the domain for our nameservers. Domain Transfers are a one-time fee, priced at the one (1) year rate for the appropriate Top Level Domain and include an automatic one-year extension of the domain's expiration upon completion of the transfer.
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.
When you buy a Premium Domain name, you are also buying strong branding potential, high recall, and the ability to attract more traffic to your site. Finding a relevant domain name to your business will provide you a storefront online, allowing your customers the most access to your products as possible. Your domain name is an investment that is easy to map back to success, and the perfect available domain name is just around the corner.
Keep in mind, however, that free domain names are usually free only for one or two years, after which the registrar will bill you for the annual or biennial fee. In other words, the provider of the free domain name pays only for the first billing from the registrar. Also take note of whether or not the provider charges a fee for setting up a domain name. Most services offer to transfer an existing domain name to their servers at no cost, but sometimes you'll find a setup fee over and above the registrar's fee.
My personal preference is to register the name directly with a domain name registrar rather than through my web host. I've heard stories, in the past, of less-than-reputable web hosts that registered the domain under their own name, making them the owner of the domain rather than you (although I don't know if such web hosts still exist today). Registering direct with a domain name registrar allows me to make sure that I am registered as the owner, the administrative and technical contacts. Being the owner is vital — if someone else places himself as the owner (such as your web host), he can always decide to charge you some exorbitant fee for the use of the name later, and there is little you can do. The various other contacts are less vital, but may still play important roles, depending on your registrar. For example, for some registrars, the administrative contact's approval is required before a domain name is transferred out of a web host (or at least, it used to be). If he/she cannot be contacted, the technical contact is used.
Avoid having numbers in your domain name. People can get confused about whether the numbers is a digit (3) or a word (three). If you want a number in your domain name because there’s a number in your company name, buy both versions (digit and word) and redirect one to the other. Be especially wary about using the number “0” in a domain name as people may see it as the letter “O.”
DNS is essentially a database of IP addresses.  Each IP address is a series of numbers that allow computers to communicate with each other. A website is identified on a server by its IP address. Instead of your visitors having to remember an IP address to type into their browser to access your site, they instead use your domain name. When your domain is entered into their browser, DNS translates it into an IP address because that is what computers understand.Your computer is able to connect to your web hosting and show your website on the browser once the IP address is found.

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.
FatCow has one of the cheapest offers for an entire website package, with hosting and domain names for just thirty cents during your first month. After, that the price is $10.99 a month or $59.88 for the whole year, in a shared hosting package with enough bandwidth for most people. This is a limited promotion I found, but they still sell fairly well-priced packages (their "fat" options come with extras like marketing and advertising credits), and will gladly offer you perks for transferring your domains and hosting to them.
If you ever change your web host (the actual physical location of your website files), your domain name goes with you. Your regular visitors or customers who knew your site name as (say) www.thesitewizard.com would not have to be informed about a change of web address (also known as "URL"), since as far as they are concerned, the site is still at the same place. They would simply type your domain name and they'd be transparently brought to your new location.
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.
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]
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