First of all you should find a good name for your website.
Your decision should based on the name of your niche or sub-niche that you have selected.
To learn how to choose your website domain name read this article: Best 5 tips – How to choose a domain name.
Registering a name is the first step to getting your site online.
This takes only a few minutes and you will own the name as long as you pay the yearly fee.
To get information about those providers and the difference between them read the article: Best Domain name registrars.
It is very easy to register your domain name in any of them, you need to register first to have an account, and then log in your account and write your chosen domain name, so it will be checked to be sure that it is available or not (if not so you can suggest another name till it is accepted).
Finally follow the paying instructions and choose how many years (minimum is one year) you want to buy this name (in fact you rent it and not own it).