The government in the Middle Colonies was, in general, the same as the government in the other colonies. All of the colonies had the same basic governmental structure.
All of the Middle Colonies had a chief executive called a governor. In all of the colonies, the governors were appointed, not elected. Some of the Middle Colonies, like Pennsylvania, were proprietary colonies. In those colonies, the proprietor got to choose the governor but the king had to approve the choice. In the royal colonies, like New York, the king chose the governor directly.
In all of the Middle Colonies, there were bicameral legislatures. The upper house of the legislature was also appointed just like the governor. The lower house of the legislature was elected by the people. Most white men could vote in at least some elections. Some colonies, like Pennsylvania, let essentially all white men vote for their legislatures. In other colonies, like New York, only white men with a certain amount of property could vote in the legislative elections. White men with less property or even no property could vote, but only in local elections.
The Middle Colonies, then, were similar to all the other colonies in that they had appointed governors and upper houses of the legislature and they had lower legislative houses that were elected by the people.