Importance of having a domain name:

Whenever you change your web host, your domain can be the same. You'll not lose visitors and page ranks in search engine index. A domain name can also give you website credibility.

What makes a good domain name?

It's good if your domain name is same as name of your website, corporation name, brand name, web content etc. Domain name should have meanings, be easy to remember and type correctly.
About the length of domain name, there appears to be some disagreement about whether a long or short domain name is better. Short domain name is easier for human to remember and less prone to typos, while long domain names that have your site keywords in them have an advantage for search engines robots thus fare better in a number of search engines.

How to register domain name?
Think of the domain names you want to use.
Go to domain registrars and apply for the domain name.
Set the DNS IP address and name server of your host, then after 24/48 hours You can access your website through your domain name.