How do I go about setting up my own name servers?

Depends who you are registering you domains with but if you have a control panel facility you can select a nameservers option and add ns1 ns2.yourdomain.com for the domain. You will need to input the IP addresses somewhere.
Stating your registrar might help with more specific advice.

I registered through register.com

It's relatively simple at register.com - but the main thing is your hosts welcome letter becuase it should have your new NS information and the required IP#s to use.

The best people to pester about this is your host, it's also a good way to test their support ;)