Take the subway to Whitehall Terminal in Lower Manhattan. There you can board and ride the Staten Island Ferry from lower Manhattan to Staten Island and back. Make sure you go on a clear day because the ride offers a great view of the city, Statue of Liberty for a very low price.
The Ferry runs 24 hours a day/ 7 days a week in 30-minute intervals both on weekdays and on weekends. During the weekdays during rush hour, the intervals drop to 15 - 20 minutes. Make sure to check the schedules for more information at: The Staten Island Ferry