Explain process of transferring domain

I read that you can/should transfer any web domains that you have connected to your project to EF. What is the process for that exactly? And how is the re-upping that domain managed. Does the project lead pay for that and they still manage the billing/payment for that? Or does EF pay for that, and the project can secure funding for that and provide that to EF.

Thanks, just trying to understand the bookkeeping involved here.