Since Chess is such a complex and famous game, I recommend looking for the rules e.g. here
You can move a piece by clicking it and then clicking the field it should go to. For castling, move the king. For pawn promotions, you can pick a piece from a panel that will show up when applicable.
Your game will be stored and identified by the URL. So after starting a game, you can always come back to it by going to the URL you got redirected to on game start.
The AI opponent
When playing against the computer, its strength is determined mainly by the time you allow it to think. You can set this to a value between 3 and 20 seconds when starting a game.
After calculating a move, the computer will remember it for future games, so by time it will have fast responses in more situations.
- Draw by threefold repetition of a position is not detected
- When the AI opponent finds moves in its database of learned moves, it chooses it naively, sometimes missing easy winning moves or getting into loops, eventually drawing by 50-moves rule.