If you are able to use Onboard Airline Check-in (have to be flying domestically on one of the participating airlines), then you register for that program and will receive boarding passes/luggage tags and leave your bags out on the last night and won't see them until you arrive at your home airport. (If your airline participates, I highly recommend you take advantage of this program.) When you arrive at the airport you can go directly to security to get out to your gate.
If you are not participating in that program, you can leave your luggage out the last night and
DCL moves it into the terminal for you (or you can choose to keep them with you and carry them off the ship yourself). In the terminal, you have to claim your luggage and take it through customs and out to the bus. (There are porters who will help you but plan to tip them for their help.) Once at the airport, you will have to go to your airlines check-in counter to check in you and/or your bags.
DCL buses to the airport run continuously. As soon as one fills up, it will leave and they will start filling the next. You do not have to sign up for a particular bus time. As soon as you leave the ship and go through customs, head out the door (there are people directing you). You show a KTTW card because it will be marked showing you purchased DCL transfers and they will show you which bus to get on.
