I'm selling a domain to someone, but because I'm new to this -I have a question - once it's sold - how does the domain become 'theirs' and in their control? I'm using GoDaddy to manage my domains
Well, it works differently for different domain name registrars. Usually, you can just push the domain name to their account. What domain name registrar are you using ?
Haa haa. With Godaddy, you need to get a few details from the buyer like particularly their name and email address. Of course, you will need their address and phone number too but those are not that important to initiate a push. After you log in to Godaddy, select the domain name and click on 'Account Change' or 'Initiate Account Change'. Then just enter the buyer's details. Within a few hours, I believe you will be alerted via email to confirm the shift. The buyer will also be alerted to accept the domain name change. Once that is done, you will see that domain name disappear from your list of domain name and it would magically appear in theirs. As to how long the whole process would take would depend on how fast both parties confirms the move. Don't just go in and change the registrar details because some people have done that and the domain name still stayed in their account.
The process of internal transfer (free push) has been explained above. However, if you are doing an external transfer, extra fees will apply.
Just a note, if the other party does not have a GoDaddy account, it will be created for them. They just need to stay at least 60 days with GoDaddy before they can move the domain name to other domain name registrar. However, if they want to stay with GoDaddy, it would be able to stay for free till the end of the domain name registration term.