I went through this process back in February. It's mostly painless transferring to godaddy.
Basically, you have to do the following:
Pre transfer:
Ensure the domain is unlocked on current nameserver
Ensure you are the contact for owner/administrator
To transfer:
Go through the process of buying a transferred domain name from godaddy
An email should be sent to the administrative contact (which should be you, if you've followed the steps.)
Follow the link or instructions in the email
Log into godaddy and make the attempt to transfer the domain name.
Should be done, but pay attention to your email to ensure there are no errors in transferring.
There should be NO downtime at all. If you understand domain name propagation, then you'll know that it's merely a process of updating any records with recent change. Since the IP of your host and the nameservers stay the same through the process, there is never a time where the records are blank or missing.