Aim: To capture as many squares as possible.

How to start: You start owning the square with a green border. You can invade squares next to this square by clicking on the square you wish to invade and choosing "invade" at the top.
Each time you invade a square it costs 10 credits (you can see how many credits you have in the top right). To earn more credits, click on other squares. Each click earns you 2 credits. For every other player that clicks on one of your squares, you get 5 credits.
The more squares you own, the more often people will click on your squares, so the more credits you will get, and the more squares you can invade.

More Advanced:
Red Square: The square which is currently selected. Options for this square are shown in the action bar near the top.
Changing Colour: Click on one of your squares (one with a green border) and choose a colour from the action bar at the top. The selected square will change colour.
Choosing a message: Click on one of your squares (one with a green border), type in a new message at the top and click the "Go!" button. This message will be displayed whenever someone clicks on that square.
Invade: Makes you the owner of the selected square. You can only invade squares adjacent to ones you currently own. Costs 10 credits.
Bombard: Destroys the colour and message of a square. Square becomes no-mans-land (no owner). Cost: 20 credits.
Paratroop: The same as invade, but any square can be targeted, not only ones adjacent to your squares. Cost: 60 credits.

Any more questiosn, check the FAQ or post on the forum.