Rock breaks scissors. Scissors cut paper. Paper wraps rock.

Score as many points as you can until you have no more possible moves. Make room for new pieces by removing old ones. Squares are removed when you wrap a weaker piece between two stronger ones. Since scissors cut paper, having scissors, paper, and scissors all in a row or column together will cause the whole set to disappear. Similar for combinations of paper-rock-paper or rock-scissors-rock.

If you place your pieces right, you might be able to remove pieces from multiple rows or columns at the same time.

After you master the 3-way game, move up to the 4-way Elephant-Dog-Cat-Mouse. That fourth piece makes it harder to get the combinations you want so the board could fill up faster.