Most of the major battles in the war happened after the signing of the Declaration of Independance
There were many little battles and skirmishes fought throughout the war, but there were few large scale battles in the war: Lexington and Concord, Bushy Run, Trenton, Philadelphia, and Yorktown, just to name a few.
A turn-around battle in the war was the battle of Trenton, in which, on Christmas Day, George Washington and his troops crossed the Delaware River to defeat the British Mercenaries.
The Continental Army took refuge from the British at a place called Valley Forge, Pennsylvania. That winter was especially brutal. Men from the army would freeze to death, and get frostbite because of lack of equipment, and clothing. There was also lack of food. Men would go hungry for days. By that spring, Washington's Army was two-thirds the size that it was the year before.