Bishops: Sit on either side of the King and Queen. They have pointy things on the top. They can move however far they want without hitting another piece* in diagonals.
Queen: Sits by the king on her color (ex. if you're playing with black and white pieces, the black queen would be on a black square at the start of the game, and the white queen would be on a red square at the start of the game, etc). She can move in any direction for as many spaces as she wants before hitting another piece*.
King: Sits next to the queen. He has a little cross thingy on top of him. He can move in any direction, one space. If one of the opponent's pieces is in a position where they could get the king but if the king or another piece were to move in a certain place, the king would not be vulnerable, they must say 'check'. If one of their pieces is in a position where they can get the king no matter what, whether he moves or not, they say 'check mate', and usually the game is over after the next turn.
Hope that helps!
P.S. Sorry I forgot to add this before. My *s just mean that they can hit another piece, but then they capture it and can't go any farther. But that's just sorta assumed in chess.