To buy a domain you can visit sites like domain.com and GoDaddy and they will charge you around 14.99 a year typically. Buying a domain does not automatically give you a hosting service you will need to buy that separately but most websites can offer a domain and web hosting as a package that could also make it cheaper.
When buying your domain you need to check for trademark infringement so try to avoid registering a domain similar to popular, well-established brands (There are online tools to help). Make sure that you do not use confusing characters like – – as it would be hard to remember and avoid using numbers too as when you tell someone two they could either spell it two or with the number 2. Try to buy a short domain as it is easier to remember, the whole point of a domain name is to avoid remembering the number format so ensure that the name is easy to remember.
You will have to ensure you read your domain contract before you buy the domain as some registrars can have clauses that let the registrar delete your domain name for no apparent reason. All registrars reserve the right to make changes to the registration agreement whenever they wish and without letting you know so it could be crucial that you check your registrar out properly before making the investment.