What is a domain name:
A label that identifies a network domain: a distinct group of computers under a central administration or authority.

Why would you want one?
1. Accessing remote computer by typing letters instead of IP addresses. 
2. Email addresses that have @your_domain_name   at the end
3. Unlimited and free subdomains

Domain name availability 
google.com has already been taken, how to find what’s taken and what’s not? 
Google is popular in terms of search domains.google.com

Understanding levels of domain

1st level
1st level
2nd level
2nd level
3rd level
3rd level
www.symbolics.com
<span><font face=”Verdana” style=”font-size: 30px”>www.symbolics.com</font></span>

1st level domain name few examples
.com is popular, but hard to find a short available name
.co.uk still has short names available, but little expensive
.info is cheaper and many short names are still available
*Many other options are available too, look around on the domains.google.com

2nd level domain name
Can be anything you like, as long as it is still on sale. 

Few tips on the choice:
– It has to be simple to type
– It has to be short
– It’s better to have keywords in it
– It’s better to be memorable 

3rd and other levels 
Once you buy 2nd level, all the other levels are yours too and free

When you’ve found “the one”, time to buy.

Few options to buy from:
godaddy.com
domains.google.com
www.cloudflare.com/products/registrar/