From Central or Wynyard in the city, any bus with the number between 184 and 190 will go through Narrabeen. The express buses (e.g. E87, E88) might not stop at Narrabeen (those that don't should say 'First Stop Mona Vale' on them), though all limited stops buses (e.g. L90) should. Ask the driver to be sure.
Narrabeen Beach is probably the most famous Sydney beach north of Manly due to its appearance in the [http://en.wikipedia.org/wiki/Beach_Boys| Beach Boys]' song [http://en.wikipedia.org/wiki/Surfin%27_USA| Surfin' USA] and the holding of professional surfing events here in the past.
There are really two sections to the beach. North Narrabeen, which is close to the Warriewood headland and which flows into a lagoon, is best for families as kids can play on the dunes near the lagoon and swim there if the surf is too strong. This part of the beach, reached via Old Pittwater Road, is very close to a camping ground. Further south along the same road is Narrabeen beach, which is popular with surfers and kite surfers.
If you fancy an outing on the lagoon, you can hire kayaks and other water craft. Ask at the camping ground for further information.
If you're roughing it, there is a large and popular camping ground close to the beach near Warriewood headland. There are both camping and caravan facilities there.