How were most governments in the American colonies organized?

The first American colony was Virginia. Virginia was granted a royal charter to found a colony, with rule of the colony being granted to an elected legislature and a governor appointed by the king. The legislators in the colony legislature could only be elected by property-holding males. The remaining colonies also received royal charters and established governments that were of a similar nature to that found in Virginia. Importantly, the legislatures did not have the same powers that state legislatures or Congress have today, because each colony was supposed to be under the direct rule of the king. The governors, as the kings' direct representatives, were meant to be the more powerful arm of government, though power of the legislatures to control the payment of the governor generally allowed for a powerful influence.
New England was slightly different, because the initial Plymouth colony was settled by individuals who initially sought Virginia but landed in Massachusetts. Since Massachusetts was outside of the established border of the Virginia colony, the Plymouth settlers created the Mayflower Compact and essentially established self-rule. When Massachusetts later became an established colony, it was provide a royal charter with a similar form of government to the other colonies, though the New England colonies retained more desire for self-rule and engaged in more direct action within towns and villages.