Democrat point is the spot in Robert Moses.
From the Sagitkos parkway make a right onto the Robert moses road, and take it to the end (going west) There is a dead end with a checkpoint and an air-up station as well.. So you just need to bring a hose with you to air up your tires after driving on the beach.
Permit is good from April 1st through December 31st for $49.. Just keep in mind that it is a FISHING permit, not and offroading permit. You must have the required equipment in your truck or they will not let you onto the beach.. And yes, they do check every truck, even once you're on the beach the State park police check up on you.