I haven't had to call them myself, but I've heard that godaddy's phone support isn't bad (though for the record I've heard plenty of bad stuff too). I expect that you could just call godaddy, tell them what you want to do and let them take care of it.
When I changed hosts I told the old host that I wanted to cancel service on a certain date and the new host that I wanted to start service on that same date and that I already had a domain. It was really easy!