what is the process of getting a domain name registered of your choice ?

[J]

whomever you choose to search for the domain you want, be prepared to register it with them immediately.

registrars use to register searched domains if the searcher did not take it, thought the practice had ceased, but testing shows its still alive and well

register.com runs specials for new customers at 50 cents usd for a dot com, just remember to transfer it to a new registrar before the 12 months are up as the renewal is high.