The colonists basically lived under the British rule. The British parliament passed some of the laws for the colonies, mostly the ones dealing with trade. They were known as the Navigation Acts. Sometimes, decisions of colonial courts were appealed to England. Pretty soon, the colonists rejected the idea that they were following the laws taken from the British government. Usually, the colonists ignored the British laws. This would lead to a conflict between the two because of their independent attitude.
One example of the conflicts would be the Boston Tea Party. The colonists tried to refuse taxation on tea, so they tossed the tea into the Boston Harbor.
In the mid-1700's Britain tightened its control over the colonies. They passed laws that taxed the colonists and further restricted their freedom. Because the colonists had gotten used to governing themselves, they resented Britain interfering with their business. The beginning of the American Revolution began when Virginia declared its independence in the Virginia Declaration of Rights. Friction built up and on April 19, 1776, the Revolutionary War broke out.
By July 4, 1776, the colonists declared their independence. It wasn't until 1783 that they defeated the British, though.