There are two main areas you might wish to look at in answering this: tactics and strategy.
In discussions of warfare, the term tactics usually means the specific procedures used on an individual battlefield in order to gain victory. Strategy usually refers to the large-scale plan the leadership, either military or civilian, designs in order to win a war. In tactics during the Revolutionary War, the Americans often did unorthodox things the British were unprepared for. Even with Britain's experience in the French and Indian War twenty years earlier, their commanders and troops were trained in the basic style of European warfare in which there were set-piece battles. The term guerrilla warfare had not even to come into use until the Napoleonic wars. In the Revolutionary War, Americans used tactics such as shooting at the British (as during the retreat from Concord on the first day of the war) from farmhouses and concealed places in the terrain which, throughout the colonies, was at that time still more densely forested than Europe. In some battles American commanders ordered their men to shoot at the British officers, which was out of bounds according to European military protocol.
The question of strategy is even more significant. Washington knew that the key to winning the war was to keep his army intact and functioning. He is often described as prosecuting a "Fabian" strategy, largely defensive in nature (the term derives from the name of the Roman general Fabius in the Second Punic War), avoiding open battle whenever possible but wearing the British down by making them pursue him. The British could take over territory, but as long as they could not destroy Washington's army and the other American military units, the rebellion would go on. The alliance formed in 1778 with France was also crucial. France not only sent an army and a fleet to help the American cause, but huge amounts of arms, ammunition, and cash. The British Parliament and even the military leaders were divided on the question of whether the war should have even been fought in the first place. The Americans knew that if the war lasted long enough, the British would decide it was too costly to continue the fight, and Parliament would vote to cut off the funding for the war. This was exactly what happened after the British debacle at Yorktown in October, 1781, effectively the end of the war, though the treaty recognising the independence of the colonies was not signed until two years later. Both tactics and strategy had worked for the Americans.