Crazyhouse is Orthodox Chess in every respect but one: a captured piece is not out of the game. It changes sides, and its captor may later place it back on the board, anywhere, as a whole move. Nothing else changes - the pieces move as they always did, castling and en passant are unchanged, and the game is won by checkmate.
The pieces waiting to be played sit in the two holdings, one column on each side of the board. A number on a holding square says how many of that kind are held.
A drop is a move like any other: instead of moving a piece, the player takes one from the holding and places it on any empty square. Four rules govern it:
A Rook that has been dropped on its corner square may not castle: castling asks for a Rook that has never left home, and this one has.
A Pawn reaching the last rank promotes as usual. But a promoted piece remembers what it was: captured, it returns to the holding as a Pawn, not as the Queen or Rook it had become.
The pieces are not worth what they are worth in Chess. Material is never gone, only lent, so an exchange that wins a Pawn also arms the opponent with one. Attacks are far quicker and far harder to answer: a hole near the King is not a long-term weakness but an immediate one, since a piece can appear on it without having to travel there. Pawns and Knights gain in value; Rooks, Bishops and the Queen lose some, having less open board to work with.