We have added the DDP 2x this year when we rented DVC points. Once in 1/07 at SSR and for our upcoming Oct trip at AKV. As you already seem to be aware, the member has to add the plan for you. When you check in, the CM will know you have the DDP. You will receive a booklet explaining the DDP, where you can use it, etc. at checkin as well. You will pay for the DDP at check out. Your room key will house your DDP points, and not your park tickets in your case, so you hand that over when you eat out. You will receive a receipt after each meal, letting you know how many credits you have remaining. Disney really makes the whole thing easy! I think in instances where a person has a package through WDW, your park tickets/room key/DDP might be on the same card (someone will likely correct me if I am wrong about this), but you purchased your park tickets separate.
Oh, and your question is not a dumb one, by the way! Enjoy your trip!!