First for some basics about domain names see this site

domains.org and or aboutdomains.com explain some basics what a domain name is and why you might need one.

Always look for a short name that is easy to remember and easy to spell, if your lucky and your company name is available go for it or find a name that in short describes what your doing or what your site is about.

 

How to find the right domain name for your website:

To find the right domain name is not that easy since it seams that most domain names you probably want seam to be already taken. However there are some good tools and sites that can help you with this task.

Here are some websites that can help you finding a domain name:

DNwiz.com
Use the Wizard to search for domain names using multiple options. You can combine keywords, check only certain extensions, insert hyphens, and more!

Find deleted domain names here and here via domain name keyword search and good info on domains also here at whois source.

 

How to register a domain name:

Once you found a name you like you need to register your domain name, a domain name registration is normally paid per year or for multiple years, the yearly fee for domain registration can be from around US $ 10.00 on upwards depending what service you use or what type of domain you want to register. There are numerous web companies out there that offer domain name registration services

I use lately Namescheap for domain name registration and found their service easy to use and cost is ok starting at only US $ 8.88 per year. Name cheap also has some features to let you search for the right domain names and payments are done easily via credit card. More domain name registration services and domain name resources can be found here in the google directory.

Once you have registered your domain you need to set the domain name server (DNS) information in your account so the domain name points to the hosting company you are using, your hosting company can give you this information. Your hosting company can also help you if you need any more help with the registration of your domain names.