The pawn can move 2 spaces on its first turn and can only move one space after your first move with it. When It reaches the end it can promote to a Queen, Rook, Bishop, or Knight.
The rook moves horizontally and vertically. If your king and rook haven't moved, and there are a few empty spaces between them, they can do a move called a castle.
The bishop moves diagonally
The knight can only move in an L position
The Queen is a combination of the bishop and rook, so it can move diagonally, vertically, and horizontally.
The king is the piece you do not want to lose. It can also move to a square around it to avoid a check, but when the king has no where while being checked its call checkmate meaning you lose.