There are plenty places to park and walk up onto the beach. It is basically like any type of surf fishing. You have to park in front of the dunes and then hike it up a path over the dunes. No different than any other beach. The area marked A10/10 is a very popular location to go up. However, the beach is always changing so one day there could be great structure around A10 and the next day you may have to move on. There is certainly lots of areas to fish along the 13 or so miles of beach. It is just about the only place to fish during daytime now that the summer is here, as well.
You can fish just about anywhere, except the bathing beaches. The park is open for fishing 24x7, as long as you are actively fishing. There isn't any additional passes needed if you are walking onto the beach, just the regular admission fee, charged per vehicle, which is $6 weekdays and $10 weekends. There is an additional "beach buggy" permit needed.
Good luck. I think if you give it a try, you won't be disappointed. The only downfalls to the Park are that it does get very crowded this time of year, especially on the weekends. Other than that, it is a great place!