Each of the 6 different kinds of pieces moves differently. Pieces cannot move through other pieces (though the knight can jump over other pieces), and can never move onto a square with one of their own pieces. However, they can be moved to take the place of an opponent's piece which is then captured. Pieces are generally moved into positions where they can capture other pieces (by landing on their square and then replacing them), defend their own pieces in case of capture, or control important squares in the game.
The Queen
The Queen can move as far as possible as long as she
does not move through any of her own pieces. And,
like with all pieces, if the Queen captures an opponent's
piece her move is over.

The Queen is the most powerful piece in Chess.
If moved she can do it in any one straight direction:
forward, backward, sideways, or diagonally, as far
as possible.

The Rook
And, like all pieces, the Rook can never move onto a square
with one of its own pieces. However, it can be moved to
take the place of an opponent's piece and capture it.

The Rook may move as far as it wants, but only
forward, backward, and to the sides.

Movements of the Bishop and the Knight.