It all depends on what registrar you are at.
Most registrars offer free accounts (GoDaddy, Enom, Dotster, etc...) that you can "push" a domain name to. For places like Enom, Dotster, etc. you will only need to get the username of the user you wish to send the domain to.
For GoDaddy, they have a longer and more complicated process, which requires you to get most if not all of the contact information of the person you wish to send the domain name to. This is a fraud prevention measure instated by GoDaddy.
I have a lot of names between Enom and GoDaddy and prefer Enom at the moment. I have transferred some of my Dotster names to my Enom account, which is another method you can use to transfer the domain name to a different registrar upon them winning the domain name in your auction.
You will ask them to make an account if they do not already have one at their registrar of choice (which if it's their registrar of choice, they most likely already have one

). Then, they will put in a transfer request for the domain name they have won on eBay. This will go through the registry and come to your end, asking you to approve or disapprove this domain name transfer. Once you approve, it can take anywhere from 3-7 days for the domain to be full functional and appear in their account at their registrar.
Please take note that the winning bidder will get charged to transfer the domain to a new registrar, but that is between them and the new registrar. If they complain about the charges, just let them take note of the extra year they are getting with that domain once they transfer to a new registrar. The extra year only applies to domains that are transferred, not pushed.
-Steve