If you don't want to use a mouse, use the keys 123 456 789 to select the respective board or cell. QWE ASD ZXC works for noughts, and UIO JKL M,. for crosses. You can always press Backspace to undo.
As you can see, there are nine boards, each with nine cells. Each board is its own game of noughts and crosses. If you win three cells in a line, you win that board -- if you win three boards in a line, you win the game!
The golden rule, however, is that your opponent always plays in a different board. Almost always, this is your choice. If you play in the top-left cell, say, your opponent will be sent to the top-left board. Therefore to take a board, your opponent has to actually send you there - the fun of the game is using your wits to convince them to let you.
A few useful tips: