Your first task is to spend up to ten minutes searching the web for someone that you can register a domain name with. Domain names are not bought, they are registered and you pay to register domain names for a set period of time - normally from one or two years.
The rules and regulations surrounding registration of domain names can change from country to country and are also dependant on the country to which the domain name belongs. The registrar you use doesn't have to be in your country, but it should be someone that you're comfortable giving your money to.
Be sure to ask your peers for advice because they will likely have valuable information that you can use in your search for a domain registrar. You may even choose to use the same one. When you've found a registrar you're happy to do business with, this task is complete.