As an experiment I moved four of my domains to hover.com, to see how painless the process is, and frankly to be sure it works, before deciding whether I should move the rest of my godaddy-registered domains.
1. Go to the Domains page on Godaddy.
3. Click the Send By Email link next to the Authorization Code item. Screen shot.
When you get the email from Godaddy acknowledging the transfer request, they say "If you want to proceed with this transfer, you may accept it immediately or do nothing. If you wish to cancel the transfer prior to the auto-complete date, you must decline it before <fiveDaysInFuture>." They give you two different links for killing the transfer, but no links to "accept it immediately."
1. Go to the My Account page on Godaddy.
2. Click on the Transfer tab. Screen shot.
4. Click on the Accept/Decline icon. Screen shot.