The desire for American independence began after the French & Indian War when the British began to pass laws the colonists did not like. They passed the Proclamation of 1763 which blocked anyone from settling the lands they won in the war. They also passed many taxes on things like stamps and tea.
The colonists were very unhappy with these new laws. Protests started to take place across the colonies. Some turned violent like the Boston Massacre. Others destroyed property like the Boston Tea Party.
The leaders in the colonies like Ben Franklin, Thomas Jefferson, & John Adams decided to meet in Philadelphia to discuss these issues. First they sent a letter to the king to try to fix it all. He rejected their letter and they decided they must declare independence.
To win independence, the Americans had to fight for it. They decided to George Washington in charge. He lost many battles early on like for NYC and Philadelphia, but he did everything he could to train his troops so they could stand up to the British.
After the Americans win at Saratoga, the French decide to help. The British begin to lose some big battles in the southern colonies like at Cowpens and head to Yorktown for help from their fleet. Instead they get trapped. Lafayette and the French fleet keep the British from escaping as Washington sieges Cornwallis and the British. They are forced to surrender.
America sends Ben Franklin, John Adams, and John Jay to negotiate for America. They are able to get the United States of America recognized by all of the major European powers and the new country gets land up to the Mississippi River.