You do NOT put your luggage out the night before. On the last morning, we go to the Windjammer for breakfast (it opens early) and go back to our cabin to brush our teeth and then just wait for the announcement. Usually it starts around 7-7:30 for Florida ports. Then you check your room - and the safe! - and walk out with your luggage. If you see your room steward, let them know you're out so they can start on your room.
They will scan you out with your seapass card and you walk the long walk to the terminal where there are two lines - passports, and birth certificates & driver's licenses. Have your passport out, but they have never looked at it, they simply hold up their tablet, scan your face and you're done. There will be Customs and Immigration officers standing around - if they want to talk to you, they'll find you. Other than that, you're done, and have a safe trip home. Easy-peasy.