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