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.
Even when you register and pay for your domain name, you won't necessarily be able to use the name for several hours or even a few days. The domain must propagate, meaning that the official domain name registry must be updated with your website's Domain Name System information. That's something that occurs on the backend without any need of input from you.

For special purposes, such as network testing, documentation, and other applications, IANA also reserves a set of special-use domain names.[15] This list contains domain names such as example, local, localhost, and test. Other top-level domain names containing trade marks are registered for corporate use. Cases include brands such as BMW, Google, and Canon.[16]

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.
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.
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 domain name consists of one or more labels, each of which is formed from the set of ASCII letters, digits, and hyphens (a-z, A-Z, 0-9, -), but not starting or ending with a hyphen. The labels are case-insensitive; for example, 'label' is equivalent to 'Label' or 'LABEL'. In the textual representation of a domain name, the labels are separated by a full stop (period).

The dispute was over the innocently-named Site Finder Service, launched by Verisign in 2003. With traffic to every .com domain going through Verisign, the Site Finder Service redirected anyone accessing an unregistered domain (via a typo, for example) to a Verisign website with sponsored links. The company argued that this was more useful to Internet users than seeing a generic error page. Whatever their reasoning, this made Verisign the de-facto owner of every unregistered domain (what else does it mean to own a domain?), and skyrocketed them from 2,500th into the top 10 most visited websites. The best part? Verisign launched this without running it past anyone.
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.[6] 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.

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.
During the 32nd International Public ICANN Meeting in Paris in 2008,[10] ICANN started a new process of TLD naming policy to take a "significant step forward on the introduction of new generic top-level domains." This program envisions the availability of many new or already proposed domains, as well as a new application and implementation process.[11] Observers believed that the new rules could result in hundreds of new top-level domains to be registered.[12] In 2012, the program commenced, and received 1930 applications.[13] By 2016, the milestone of 1000 live gTLD was reached.

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.
Domain name registration is a crucial decision for any entity planning to join the virtual arena. A domain name is an exclusive address of your website through which it is found by your target audience. The process of buying a domain name is called Domain Name Registration. As a domain registrar, BigRock has millions of domain name registrations to its credit.
Domain names serve to identify Internet resources, such as computers, networks, and services, with a text-based label that is easier to memorize than the numerical addresses used in the Internet protocols. A domain name may represent entire collections of such resources or individual instances. Individual Internet host computers use domain names as host identifiers, also called host names. The term host name is also used for the leaf labels in the domain name system, usually without further subordinate domain name space. Host names appear as a component in Uniform Resource Locators (URLs) for Internet resources such as web sites (e.g., en.wikipedia.org).