Governor's Island is open every day from May 1 to Oct 31.
Mon - Fri: 10 am - 6 pm
Sat - Sun: 10 am - 7 pm
The ferry departs from Manhattan and Brooklyn terminals, Sat and Sun usually every hour or 30 minutes 10 a.m. - 5:30 p.m. and the last boat from the island leaves at 7 p.m (6 p.m. on weekdays). However, the schedule is subject to change so you should consult the website before going.
Children under 13: free
There are some free ferry rides on weekends. See the official website for more information.