These are the steps that you need to follow in order set up your domain name:
Purchase a domain name from a registrar.
Find a DNS name server to be authoritive for your domain.
Configure your name server's DNS records for your domain.
Let your registrar know who is the authorative name server for the domain.
Getting a domain name is relatively straight forward, you find a domain name registrar, chose a name that's not already registered, and pay the fee. All of this can be done via the registrar's website. Registration is for a fixed period of time, the minimum time being one year. There are quite a few bargain registrars where the price is under US $10 per name per year, so shop around before you buy. Make sure that you chose a registrar that will allow you to configure your account online (more about that later). A list of accredited registrars can be found at ICAAN. But be aware that some of the registrars go by a different name for their bargain rate outlets, so the ICAAN list is not exhaustive. Nor does the ICAAN list cover country specific domains (such as .au for Australia or .tw for Taiwan). You can also ask around in the newsgroups for recommended registrars.
The .com, .net and .org domain names are freely available for registration by anyone. But virtually any name that's in the dictionary will have already been taken, either by someone who actually uses it, or by someone whose speculating that they can sell it to someone else at a profit. Names made from groups of words are more likely to be available. There's no way that you'll get hotel.com, but you could well find that you can get TheBrisbaneHotel.com. You have to be a bit creative. The registrar's web site will be able to tell you if the domain you want is available.
The registrars for country specific domains may be more restrictive. They may require that your domain name is the same as your company or organisation name, and the registrar may not allow these names to be sold to a third party. You are also less likely to find a bargain rate.
Getting the name is the first step, the Domain Name System (DNS) is what allows you to use it.
Once you've aquired a domain name, you have to make it point to your host site. That is to say, you have to make the name resolve to the IP address of your host computer. This is where the Domain Name System (DNS) comes in.
Computers on the internet find each other using IP addresses, but people find computers on the internet by name. The Domain Name System maps domain names to IP addresses. DNS is based on a globally distributed network of name servers. A query to a DNS name server will yield the IP address of the submitted domain. The name server is said to resolve the name to an IP address.
Your domain needs a DNS name server that's authoritive for it. Queries to this name server will produce the IP address(es) associated with your domain name.
When your web browser (or email client or whatever) tries to contact another computer on the internet, it asks the closest name server for the IP address for that computer's domain name. This name server will 'ask around' other name servers and will be directed to the name server that is authoritive for that domain. The authoritive name server will then relay the IP address back to the requesting application.
If your site has a fixed IP address, then you can host your own name server. But you'll also require a secondary name server, a backup if the primary goes down. You may find it easier to use a name server provided by a DNS service.
Your ISP might provide a DNS service, but you'll most likely have to pay for it. Your domain name registrar may also provide a name server, also possibly for a fee. But there are free DNS name servers if you look around. Google 'free DNS'. A good, free DNS service can be found at www.zoneedit.com. When you've found someone to provide a DNS service for you, create an online account with them and add your domain name to it.
The next step is to configure your name server with information about your domain.
The IP addresses associated with your domain name are held in the DNS records of your name server. You need to enter the correct IP addresses into these records.
The 'A' record lists the IP addresses for your domain. Each IP address will have one or more names associated with it, either the domain name itself, and/or associated subdomain names.
If you have a mail server its name must be in the 'A' record. This name will also have to be entered in the 'MX' record, designating it as the mail server.
Your domain can have as many subdomains as you like. Each subdomain has it's own entry in the 'A' record, its own IP address. The IP addresses can be different, or the domain and subdomains can share the same address. Two common subdomains are 'www' and 'mail'. The 'www' subdomain often shares the same address as the domain, and you'll find that you can usually use either 'www.mydomain.com' or 'mydomain.com' in your web browser. The 'mail.mydomain.com' is often the entry found in the 'MX' record.
If you have a dynamically assigned IP address, rather than a fixed one, then the DNS records must be updated whenever the address changes. This can be an automated process using a method that's refered to as 'dynamic DNS'. A program refered to as a 'DNS update client' monitors the IP address of the host. When the IP address changes, the client notifies the name server of the change. But you have to make sure that your name server allows dynamic updates.
Now you have to let the rest of the internet know how to locate the name server for your domain.
I mentioned earlier that name servers 'ask around' to find the authoritive name server for your domain. Now you have to make sure they know where to look, you have to get the location of your name server known. This is done through your domain name registrar.
It's simply a matter of providing your registrar with the names of your name servers, and the rest automatically follows from there. You should be able to configure your account online; login and make the name server entries. Notice that I've said name servers, plural. You need a secondary name server to act as a backup in case the primary one goes down or is unreachable. Normally the DNS service that you use will provide you with both a primary and secondary name server.
DNS is distributed across a hierachical world-wide network of name servers, so it takes some time before the information about the location of your nameserver propagates through the system. Allow 24 to 72 hours. Don't expect name resolution for your domain to work reliably before this time.