The two kings cannot give checkmate to each other (not even check).

Easy mate. The queen has to shrink the moving area of the king until it is restricted to the edge of the board. Then the queen can deliver the checkmate with the support of its king.

For more details, see: Wikipedia: Queen checkmate.

Easy mate. The rook has to shrink the moving area of the king until it has only two squares in the corner. The attacking king needs to support the rook meanwhile. Then the rook and the king can deliver the checkmate.

For more details, see: Wikipedia: Rook checkmate.

A single bishop and the king cannot deliver checkmate (not even if the opponent helps).

A single knight and the king cannot deliver checkmate (not even it the opponent helps).

Quite easy mate. Precondition: the two bishops moves on different coloured fields (otherwise checkmating is not possible, not even if the opponent helps – but that case can only arise by pawn underpromotion or in chess variants).

The two bishops standing on adjacent fields can close the defending king to a certain area. This area needs to be shrinked (with the support of the attacking king) until the king has only two squares in the corner. Then the three pieces can deliver the checkmate.

For more details, see: Wikipedia: Two bishops checkmate.

Difficult mate. Checkmate can only be forced in the "right" corners, i.e which has the same field colour as the bishop moves on (in the other two corners, checkmate cannot be forced). First the king has to be forced to the edge of the board (and it usually goes towards the wrong corner), then it has to be forced to the right corner, where the mate can be delivered. Effecient coordination of the three pieces is required.

For more details, see: Wikipedia: Bishop and knight checkmate.

Checkmate exists, but cannot be forced. Though the king can be forced to the corner, but it is then either stalemated, or is able to avoid being checkmated. This is partially because of the fact that whenever a knight moves, it loses all controlled fields.

Not too difficult mate. The king needs to be forced to the corner using all the four pieces (for example well-cordinated knights can make a wall), and there they can easily deliver the checkmate.

Relatively easy win. Checkmate can be delivered also with the bishop on the board, so capturing it is not necessary – it is enough to avoid the bishop's field colour. The attacker needs to force the king to the edge of the board (by near checks, with the support of the attacking king), and there the checkmate can be delivered.

Not too difficult win. Checkmate can be delivered also with the knight on the board, so capturing it is not necessary. The attacker needs to force the king to the edge of the board. Then the knight might try to prevent the mate, but finally it can only do so temporarily by sacrificing itself. The attacker should try to avoid those distances from the knight, in which it can attack pieces easily.

Very difficult. The point is to capture the rook, mostly by a fork. Therefore the rook tries to be close to its king. The attacker needs to force them into the corner, and reach the Philidor position, where the defender has no choice but to separate the rook and the king.

For more details, see: rolandbesblogs.com: Queen vs Rook.

There is no general winning strategy, but sometimes it is possible to win. The stronger side (with the rook) can win if the defending king is in the dangerous corner, i.e. the corner with the same colour as the bishop moves on. Usually the defender is able to reach the safe corner, where win cannot be forced.

For more details, see: chess.com: Rook vs Bishop

There is no general winning strategy, but sometimes it is possible to win. The stronger side (with the rook) has winning chances for example when the knight is far away from the king, and can be trapped.

For more details, see: chess.com: Rook vs Knight