Upon arriving in Vincennes on February 23, 1779, Clark's men, tired, cold, wet, and starving, were provided for by the local French inhabitants who greeted the Americans warmly. That same evening, Clark's men surrounded the fort and began to fire on it. Clark knew it would still be tricky for his small force to intimidate Hamilton into surrendering, so he employed several different strategies to strengthen his position. He gave his men orders to make noise and to fire as often and as much as they could in order to give the illusion of a much greater force. Clark also gave orders that every time the fort cannon ports opened, American riflemen should fire immediately. The British had great difficulty in successfully firing cannon shots during the battle.
In one of Clark's most controversial moves, he caught some Indian allies of the British who were returning to the fort unaware of Clark's attack. Clark had the Indians executed within view of the fort. The execution showed other Indians that the British could no longer protect them, and it signaled to Hamilton that his troops might receive the same treatment if Clark was forced to storm the fort.
Hamilton was greatly influenced by Clark's military tactics, and surrendered the fort. After only two days of fighting the Battle of Fort Sackville was over with no confirmed losses on either side.
Source: Vincennes: The British Barrier to the West
National Park Service, U.S. Department of the Interior, Public Domain