It's kind of like a game of battleship, but with the addition of a dice-based targeting system which provides more hits at the expense of precision. The objective is to destroy all of the opponent's colonies. Every turn, you first decide whether you want to make a precise shot (the Auto button), or two dice-targeted shots (the Manual button).
For Auto shots, you simply click on a square to target it. For Manual shots, 4 dice are generated which you can drag and drop into the position markers on the top and right sides of the grid to specify target coordinates. Regardless of how you target, you can then commit to your shots and start battle by clicking the GO button on the bottom right of the screen.