This is my first time walking to the Fire Island Lighthouse from the Robert Moses State park, field 5 parking lot. A quick side note: after entering the parking lot, turn left and drive all the way down until you can't go any further.
You'll see a pathway that is clearly marked, which leads to the Fire Island Lighthouse and Fire Island it self. Do be sure to bring food and water with you because there is no other place to nourish yourself for another 3.5 miles if you keep hiking beyond the lighthouse. And no, there is no food or water for purchase at the light house either.
The first light house was built on Fire Island in 1826, but due to its short stature, it was pretty much deemed useless and demolished. Since that time, the lighthouse has changed hands and design. Essentially, the light house you see today was restored in 1939 and re-lit in 1986. If you would like to read the full history of the Fire Island Lighthouse click on: History
I didn't get a chance to go inside the lighthouse, but they do offer tours and educational programs.