The quick answer is, you lease your domain name from a Domain Registrar. A person or company may lease a Domain Name for one or more years.
What is a Domain Registrar?
This humorous video from YouTube user Kieran D explains what a Domain Registrar is.
How to pick a Domain Registrar?
TechRepublic has a great article on their blog with 5 tips for choosing a registrar.
Do you have a list of some popular Domain Registrars?
Yes, below is list. It is not comprehensive but it has some of the most popular Domain Registrars. RdyToGo does not endorse or recommend any particular Domain Registrar and can usually work in connection with any Domain Registrar.