Reversi offers you three level of difficulty if you want to play against the computer.
These levels are called: Easy, Medium, and Hard. The first one is suitable for beginners, the second for casual players, and the last one should please regular players.
When configuring a new game, have a look to the second button with a down arrow; it should either be labelled Difficulty: Easy, Difficulty: Medium, Difficulty: Hard or More options. The first three possibilities indicate which one of the three levels would be used if starting a new game. In the latter case, Reversi is currently configured for a two-player game, and you should first configure that you want to play against the computer.
Once that is done, if the indicated level is not the one you want, select the button, and in the menu that appears, select Easy, Medium or Hard, as you prefer. The button will change its label accordingly.
When the indicated level is good for your, you can select the Start Game button to launch your game and play.