Each of the 13 colonies had a charter, a written agreement between the colony and the king of England or Parliament. There were three forms of charters - Royal Colonies, Charter Colonies, and Proprietary Colonies.
In the royal colonies, a colonial legislature was elected by adult men who owned property in the colony. Rather than a business owner or board of directors, the colony had a governor, appointed by the king. The legislature could pass laws, but the governor (like the business owner) could reject those laws if he felt they did not reflect the laws the king wanted enforced. The governor had British soldiers to help him enforce the king's laws. But the colonial legislature did have a weapon of their own - per the terms of the royal charters, they controlled the governor's salary. That helped them get laws passed that might not have passed otherwise.
The Charter Colonies and Proprietary Colonies were granted to businesses. All they had to do was hold a business meeting. The colonists did not actually have the right to a voice in how they were ruled. But each colony, whatever their original charter agreement, soon developed some form of democratic representative government to rule their colony.
The first legislature to be formed was the famous Virginia House of Burgesses.
There was one colony who did things a little differently. When the first pilgrims voyaged to the New World, they got lost. They were headed for the Virginia colony, but ended up in what is present day Massachusetts instead. Virginia did not control that part of the New World. No one did. Since there was no official charter to obey, the Pilgrims created their own government. They drafted the Mayflower Compact, which basically stated they would rule themselves. Although later on they became a royal colony, their system of town meetings remained the form of government in the northern colonies. That's one reason the town meeting never became popular in the middle or southern colonies. Their governments were based on written charters of agreement with the king or with parliament.