Ferries travel back and forth between Monhegan and the mainland very regularly. Your best bet is to catch one leaving from either Boothbay Harbor, New Harbor, or Port Clyde.
Because the lighthouse still hosts an active Coast Guard presence, tourists aren’t allowed to climb to the top. But, you’re free to enjoy the grounds surrounding the light tower.
While you can definitely see most of what Monhegan has to offer in one day trip, a lot of the island’s biggest fans will tell you that your trip is incomplete without an overnight stay at one of Monhegan’s inns.