You can move your king one square along in any one direction, including diagonally.
So, you can move your king either one square to the left or to the right, or one square forwards or one square backwards. Or you can move your king diagonally, either forward-left, or forward-right, or backward-left or backward-right. All in all, you can move your king to any one of up to 8 different squares depending on the direction of the move.
Of course, if your king is at the side of the board, then it will not be possible to move it in all 8 directions, as some would involve moving your king off the board, and you cannot do that! In fact, if your king is at the side of the board, then you will only have a choice of 5 squares to which your king can move, and if your king is on a corner square, then you will only have a choice of 3 squares.
You cannot move your king to any square that is being attacked by your opponent. If your king is already under attack when it is your move (this is known as being in check) then your move must involve taking it out of attack, and if you cannot do so, then you lose the game! This is called checkmate, which you will learn about later in this tutorial.
Finally, you cannot move your king to any square that is already occupied by one of your own pieces, as you cannot have 2 pieces on one square. In fact, at the start of the game, your king is completely surrounded by some of your other pieces, so that you cannot move your king on your first turn. You first have to move at least one of the other pieces around the king before you can move the king itself.
You can also capture an enemy piece with your king
In fact, a king can capture any enemy piece that is on the square to which the king is moving. All you have to do is remove the enemy piece from the board and replace it with your king.
While you king is your most important piece on the board, it is not your strongest piece, that honor falls to the queen which you will learn about next...