All movements in Yahoo! Games involve either "drag and drop" or double-clicking.

In the games that involve moving game pieces (Chess, Backgammon, Checkers, etc.), click on a game piece, hold the mouse button down, move the piece, and then let go of the mouse button.

In the games that involve placing game pieces (Go, Reversi, etc.), click on the square on which you wish to place the piece.

In the card games, select a card by double-clicking it.

Other actions (rolling dice, passing cards, etc.) are performed by clicking the appropriately labeled button.

In Pool, you can aim and shoot with the arrow keys on your keyboard or use your mouse -- left-click to aim, right-click to shoot. On a Mac, use shift-click to simulate a right-mouse button.