If you plan on entering any clubs, you buy an admission ticket at the ticket booths (if you don't already have one as part of your pass). When you enter the first club you go into, you have your ticket swiped and they give you a wristband. The wristband shows (1) that you've paid admission and (2) that you're old enough to drink. Designated drivers and underage visitors get either a different color wristband or a handstamp.
After you get your wristband, if you want to go to another club, walk out of the one you started in and just show your wristband when you walk into another. For the admission price you can visit any of the PI clubs, unless you've bought one of those one-club-only tickets (I've never bought one so dont' know how those work).
If the Adventurers Club doesn't open late, they often have some free time between 7 and 9 PM. This gets you into a couple of library shows to check things out. At 9 PM everyone without proof of admission payment (the proper wristband or handstamp) is asked to leave and purchase admission if they'd like to stay longer.