Reversi is played with two players. When playing the online version of Reversi on this site, you play as the black chips, against the computer who is playing as white. The game begins with four chips placed in the center of the 8x8 game grid. Both players have 4 possible initial moves they can make. Since you will be playing as black, the possible moves you can make at the beginning of the game are shown below.
The opening moves at the beginning of the game are all horizontal or vertical. You can place a chip anywhere there is a white chip next to it in a horizontal, vertical, or diagonal line, as long as there is a black chip in that same line, without any empty spaces in between. In the example below I demonstrate a horizontal choice you could make.
You can also place chips in diagonal positions. Below is a slightly different game board where there are 3 possible placements you can make on a diagonal axis with the white chips.
When you make a move, white chips between the black chip you just put down and another black chip is turned into a black chip. You take turns with the computer, until a chip is placed in every grid cell. If a player is unable to make a move, the other player make take a second turn. When the grid is filled, the player with the most chips on the board wins the game.