Largely through royal governors, one for each colony (such as New York, North Carolina, etc.) The royal governors, appointed by the King, would set policy for each colony based on general instructions provided by the King and by Parliament. They were backed up by a small number of staff members, by courts following British laws, by British troops garrisoned in each colony, and by a legislature elected by the citizens of each colony (such as the Virginia House of Burgesses). Members of the legislature had to be white, male, landowners, and Christian.
With such a structure, it didn't matter that instructions from London took several weeks to arrive.