This post describes how to capture pieces and the rule of drops. The drops rule is the most different system between shogi and chess.
How to Capture Pieces
The Basic Rule of Capturing Pieces
Consider the case in which some pieces are arranged around the king as shown in the lower figure. In this case, the king can move to eight squares painted pink, because the pieces around the king are opponent's.
If the king moves one square backward from the situation in the upper figure, the lance is removed from the board. The removed lance is retained in the pieces stand of the capturing player. This captured piece is "in hand" of the player with shogi term. Such an act of removing a piece is called "capture" with shogi terms.
A player must show pieces in hand to an opponent. Hiding the pieces in hand is bad-mannered, and it's called "hidden pieces (隠し駒; kakushikoma)."
Capturing a Promoted Piece
A player must turn the unpromoted side of a captured piece upward when the player places the piece on the piece stand. For example, as shown in the lower figure, a player must place an unpromoted rook on the piece stand in spite of the fact that the player captured the promoted rook.
Drops; How to Use Pieces in Hand
On any turn, a player can place a piece in hand on any empty square instead of moving a piece on the board. This is called "a drop." A player must drop a piece with unpromoted side up even if dropping on the promotion zone. For example, as shown in the lower figure, a player can drop the bishop on any square painted in pink.