Reversi allows you to play against the computer, with three different levels of difficulty. You can also decide which player, between the computer and you, will start.
When configuring a new game, have a look to the first button with a down arrow; it should either be labelled Color: Dark, Color: Light or Two players. In the two first cases, Reversi is already configured to start a game against the computer, else it would start a two-player game.
If the button is labelled Color: Dark, that means that you will do the first move. Of course, Color: Light means that it will be the computer.
If the button indicates Two players, select it, and in the menu that appears, select Play first (Dark) if you want to start the game, or Play second (Light) if you want the computer to start. The button will change its label to Color: Dark in the former case, and to Color: Light in the latter.
Once you have configured Reversi to play a game against the computer, you may change the computer level.