When you do sign up with a hosting company, they will supply you with some nameserver details along the lines of ns1.myhost.com and ns2.myhost.com.
Armed with that information, you will go to register.com, sign-in as a member, and look for something like 'manage domains' where you will be able to modify the default nameserver information (DNS). The domain name may currently have something like dns1.register.com & dns2.register.com.
Once you have done that small task, after a propagation delay of around 24-72 hours, your domain will point to your new host and will appear to the rest of the world.
All being well, you hosting company will provide some detail like this and hopefully more.