There's not a 'push' like you have at eNom and some other registrars, but it's still easy.
Once logged in, and at the 'Manage Domains' screen, just click the box next to the name you want to transfer, then hit the 'Change Account' button at the top menu section above your list of names. This will take you to a screen where you need to fill in the new owner's contact information. You can put in temporary stuff if you don't have (or don't want to ask for) their address, phone number etc.
The key is to have their valid email address. Hit the 'Save Changes' button, and then GoDaddy will send the new owner an email message with directions and codes to complete the transfer.
EDIT: Dave beat me by a few seconds. :p