I am going to assume that you have 1) chosen a topic you are knowledgable and passionate about, 2) have done keyword research and have a list of keywords with high volume and low competition and 3) an interest in making money with your blog.
Once you have identified keywords that have potential to generate traffic for your website, your next step is to research the available domains. A Domain is simply a name that is assigned to a specific Internet Protocol or IP address by the Domain Name System or DNS. It is much easier for an internet user to remember a name than an IP address.
Search for Available Domain Names
It can be difficult to find a domain name that ends in the popular .com, .net, or .org TLD. Domainr helps you find other domain name configurations that have made sites like del.icio.us popular.
Domain Tools is a popular site that not only can help you to search for available domain names but also information about other websites using the Whois search. You can even see the domain name ownership history, something that might be useful if you are considering purchasing a domain. Domain Tools also has free ping, traceroot, and DNS Lookup services.
Dot-o-mator is a domain name service that suggests domain names based on prefixes and suffixes (keywords) that you enter. You can also use a category of prefixes like (tech or games) and suffixes like (hardware or Web 2.0 words) and a list of suggested site names will be generated.
dnScoop is useful if the domain name you want is “for sale” and you are interested in trying to determine a fair value. dnScoop tries to determine a value based on site traffic, links pointing to the domain, and other factors.
Register Domain Name
Once you decide on a domain name you will need to register it with a domain registrar and I would highly recommend using GoDaddy to register your domain. There are literally thousands of domain name registrars out there and you should use ICANN to verify if your registrar is accredited.
The actual process of registering a domain name is very simple. You create an account with your domain name registrar, enter the name of your domain, and pay a fee. You have the option of renewing your registration automatically and I recommend this option.
You will also have the option for private registration for an extra fee, usually around $10 per year. I highly recommend Private Registration as this will keep your name, address, email, and phone number from being published in the Whois database.