That's a map of the whole route after you get off the parkway. Take exit 82 (not 82A) off the Parkway South. As far as I can tell it's exit 82 if you're going parkway north as well. You're looking for route 37 east.
-Take 37 east over the bridge.
-Take the first exit on the right (not the first right turn though, there are side streets before the actual exit) towards Island Beach State park (from the map it looks like you're getting onto 35 South but I've never seen any actual signs for that there)
-Follow the road on and on and on until you get to the gates of Island Beach State Park. Don't stop until you get there.
Some more helpful maps:
It was fun..I kept hitting east on the map on the website and eventually the "map" turned blue..ocean?