Go to the Manhattan terminal for the Staten Island ferry, located at the southern tip of the island just east of Battery Park. The closet subway stops are at South Ferry station and Whitehall St. station.
Enter the terminal waiting area upstairs. When the ferry arrives and is ready for you to board you will know. Just listen for the big doors to open and follow the waiting crowd. The ideal time to take the ferry for sightseeing purposes is during the evening rush hour in the winter and just after the evening rush hour in the summer, so you can experience daylight views going across the harbor and nighttime views coming back.
Go out on deck. Most everyone else on the ferry will be actual day-to-day commuters, not tourists. They will all go sit toward the front of boat after entering, eager to get off when it reaches the other side of the harbor. This is the point where you want to stop following the crowd. Stay at the back of the boat. When the boat gets going, walk out onto the back deck so you can see the best views as it crosses the harbor.
Look to your left to see the Statue of Liberty and Ellis Island on your way to Staten Island. There is a snack bar in the middle of the boat and the whole ride takes about an hour round-trip. You can leave the ferry and catch a different boat for your return journey or stay on the boat and return right away.
