Fulong (福隆) is a town in Taipei County. It has an excellent beach and is a popular place to surf.
By train: The train station is within easy walking distance to the beach. It takes about an hour to get to Fulong from Taipei. You want to catch the express as it only takes 70 minutes. The local is much longer. The express train doesn't leave so often though and you may have to wait for it.
By bus: Buses from points north and south ply the route along Provincial Highway 2.
Rent a bike for NT$100 for the day at the Giant bike shop right next to the train station (this was November, might cost more in the summer) or other bike shops, with older more local looking bikes, rent for about half the price.
Walk or bike through the Old Caoling Railway Tunnel. Take a right on the street immediately in front of the railway station. About a 10 minute bike ride will get you to the tunnel entrance on the right just after crossing the railroad tracks. The ride through the tunnel (about 10-15 minutes) takes you to the east coast and a nice view of Turtle island. The tunnel is lit, but get a bike with lights so others can see you coming.
The Longmen Campground is about ten minutes' walk north of downtown along the east side of the highway. It's rather pricey for a campground - NT$800 per site and an additional NT$70 per person - but if you get a group together you can save. The facilities are excellent. Bring your own tents.
The train station is at the end of a short side street that meets the highway at the traffic light.
Across the side street next to the 7-11, at the corner of the rest area parking lot, is a small shelter where you can wait for northbound buses.