The Americans were moving to the north end of the long, narrow island, and crossing the narrow water to the mainland. The north end of the island is dominated by a hill, on top of which was a fort built by the British but now in American hands. The Americans took position on this hill, and defended it successfully against several British attacks. During the night, they managed to slip away to the mainland. The First Rhode Island had an important role in this fight.
Today there is a monument at the site of the action.
Even though the Americans totally failed to take the island, and were in full retreat when the battle occurred, it is often considered an American victory, because the Americans successfully held off a professional army. Let me know if you want some recommended reading. When the 1776 enlistments were about up, the RI General Assembly voted to raise two regiments numbering 1,430 men combined. The recruiting did not go well. In spite of additional bounties offered, by February 1777, only 50 men had enlisted in the two regiments.