Note that your opponent does not have to take the piece but there is no advantage to not taking the piece. After the Nf3 point, the opening can go in any direction, but white will eventually seek to play d4, resulting in the complete control of the center of the board.
2 Bishops and a King. 1 Rook and a King. Two rook and A King. A Queen and A King. A Queen, A Rook and a King. 1 Knight, 1 Bishop, and a King. The Knight, Bishop, and King vs. King checkmate is complicated, and some Masters don’t even know it, but the other mentioned checkmates are simple.
First move the rook to the rank ahead of the enemy king. This will confine the king to a certain number of squares. Advance the king to obtain opposition when your king is in front of the opponent’s. When he moves away, you will need to make a waiting move, just move the rook one square over. He will move the king away from your king. When the kings are opposite each other, check him with the rook, and then repeat the process until he is on the back rank, where check becomes checkmate. The Queen checkmate is identical, but you must be careful not to stalemate.