Color the map with four colors, so that no two adjacent regions have the same color. (Regions touching at only one corner do not count as adjacent.) There is a unique coloring consistent with the colored regions you are already given.
Drag from a colored region to a blank one to color the latter the same color as the former. Drag from outside the grid into a region to erase its color. (You cannot change the colors of the regions you are given at the start of the game.)
Right-drag from a colored region to a blank one to add dots marking the latter region as possibly the same color as the former, or to remove those dots again.