So you and your partner play two other people in two separate games. One of you takes White, the other takes Black. If you capture the opponet’s pieces, you pass it to your partner, who, subject to various rules, can drop the piece on an empty square on their move in the place of making a move. The game customarily finishes when one player on one board is checkmated.
I had this lit bughouse match at the chess club once when I checkmated the opposing king with three bishops and quadrupled isolated passed centered e-pawns.