I have not done back to back post 9/11 but I can't imagine it has changed much. As long as you have the same cabin for both cruises you simply check in once and check out once. On the day that everyone else is getting off the ship after the first cruise is done you will be allowed to stay put in your cabin and on the ship if you like. If you want to get off the ship for a bit then you just let them know and they will give you an 'in transit card' to get on and off as you please. You will keep your keycard as you will need that and your 'in transit card' to get off the ship and you will also have to use the crew entrance to do so. (The main passenger exits are controlled by immigration and customs so you can't mess with them.)
It is kind of a fun feeling on that last night of the first cruise as everyone is scrambling to get packed, pay the bill, put their suitcases in the hall, etc. you get to relax because you aren't going anywhere!
You do want to remember to tip everyone after the first weeks cruise though. You may not have the same waiter and busboy for the second week. (Probably won't in fact.) You can check with your cabin steward as some ships keep the same cabins from cruise to cruise while others change each time. But also remember that these people live for their tips so even if you have the same room steward it might be nice to go ahead and tip him for the first week after it is done. Often when a ship pulls into their home port they employees get off to deposit money, wire it home, etc.
Keep in mind that after the second cruise when you do disembark you are only allowed the duties and custom-free things for one cruise worth. Just because you were on two cruises does not mean you are allowed to bring back twice as much.