No, you get a card with a tab on it for each attraction that has a FP option at the park you are in. Once you use the tab, that is it for that ride (you can still get regular fast passes, but you can only use a Dream Fast Pass once per attraction). You will break off the tab and hand it to the person that collects fast passes.
We won ones in MK and I believe there were 9 tabs on it.
We won the dream fastpass at Magic Kingdom and it was just for big ticket rides for the most part. Oh, and you only got to use it once at each ride. We didn't even really use ours because the lines were so short. I think we actually only used it for BTMRR.
We got them for Epcot. The CM's are supposed to take the tabs off but they didn't do that at Test Track and Mission Space. I guess it just depends on the CM's.
We won DFP in Epcot and it was very slow that day so sometimes the CM's would not take the tab off and to use it again when it was busier. They let us ride Soarin' twice since the wait was less then 5 mins....lol Test Track we did 3 times due to short waits.
Total luck of the draw. You can't "do" anything to win one. The times and places they will be handed out are predetermined by an accounting firm. The Dream Team doesn't know what it will be doing until it is time to do it.