If you want to register a .uk domain name I generally use www.freeparking.co.uk. Most companies that register domain names offer a similar service.
In the Freeparking example, go to the website and enter the web address you are interested in into the "is your domain name available" box and then click "Speed Search". If your domain name is already taken you can use the advanced search to find alternatives - if you want your website address to contain a number of words enter a word into each box in the advanced search section and then click onto "Advanced". A list of all available domains (with our without a hyphen separating them) will be shown. For example if you wanted to register a site to do with "internet marketing" you could enter "internet" into the first box and then "marketing" into the second and leave the third blank and then click "Advanced".
The Freeparking site can also be used to check other domain names ending in .com, .net etc.
