So, your timeline might be a bit scrambled, which is fine -- the Revolutionary War is often not covered well in American schools, let alone in other places.

The official Declaration of Independence which was voted on by the Continental Congress in July of 1776 came almost a year after the first shots of the war were fired, in April of 1775. I wrote about the fighting at Lexington and Concord that day, and the running fight back to Boston, in this answer, which also includes information on the run-up to the war and the tensions that existed in British North America. After the Declaration of Independence, the British did send more forces to the Americas (and more had been on the way before the Declaration in any case), and the war continued with fighting throughout the colonies through 1781, when the British surrendered at Yorktown; the conflict officially ended when the British recognized American independence with the treaty of Paris in 1783. There's much more that can be said, so you may want to check out this section of our FAQ.