The King

may move one square in any direction, so long as no piece is blocking his path

The Queen

may move any number of square, straight or diagonally in any direction

The Rook

may move in a straight line, any number of squares, horizontally or vertically

The Bishop

may move any number of squares diagonally

The Knight

can jump to any square in L shape. This is the only piece that can jump over a piece in its way.

The Pawn

on its first move may move either one or two squares straightforward. After its first move it may only advance one square at a time.