I want to start paying yahoo, instead of Reister.com. How do I transfer over?

Register.com is a government endowed monopoly. Yahoo may host your domain name just like any other service provider, but you can't get away from monopoly control it you want to keep your own domain name. Sad but true. But if register.com is your service provider, you can switch easily. You will still have to pay fro your domain name at one place, pay for you isp at another place. There are only a few monopolies controling registration, you might be able to re-register with one of the other 3 or 4 companies allowed by government.

You cannot actually do a registrar transfer with Yahoo.