I believe it is a week before your cruise, you can do a pre-checkin online. I recommend doing this to set up your onboard accounts. Then the day of the cruise, all you do is give them your passport, take your picture, sign something and you are on your way.
We did this for the Oasis and were through checkin in about 10 minutes.
Carnival Triumph - Spring Break Cruise - 2006
Carnival Victory - Birthday/Summer Cruise - 2007
Oasis of the Seas - Group Cruise - 2010