You can buy your domain through a registrar, the company that manages the reservation of domain names. As an example, EuroDNS is a registrar.
The registrar takes care of the initial registration process, but also provides support with domain renewal or transfer. They are in charge of providing technical support to registrants experiencing issues related to their domain.
No registrar sells all domain extensions, so you may have to check more than one registrar to find your preferred TLD. We recommend comparing the offers from several registrars whose websites you can easily find on Google.