Bishop & Knight

Pattern # 9 This technique is explained in ebook Fundamental Chess Patterns

The sequence to mate with Bishop & Knight. No need to deeply understand it, it took Judith Polgar 23 moves, starting from a favourable position. It would be a tough task to remember the technique, more difficult to apply it properly within 50 moves, and the chance to meet such an endgame in a lifetime is very scarce.

Additional different patterns can be found on this page of mine: Patterns

Some endgame manuals will give you the complete procedure to achieve a mate: I find that difficult to understand, to remember and to apply properly within 50 moves. Therefore a simplified procedure for the winning side follows, but if the hour is late, and you understand your opponent knows how to defend, I suggest a draw:
a - You herd the enemy king against the edge of the board, using your chess knowledge.
b - The opponent (if he kows, or after a little reasoning) will move towards the corner which is of the opposite color square as your bishop. As he can't be stopped from doing this, you follow him towards the "safe" corner.
c - Then you (try to) push him toward the mating corner, preventing his return to the safe corner, keeping him constantly trapped against the edge.
d - As it's not possible to just force the king along the side all the way to his doom, at a certain point you have to allow the enemy king to escape the edge of the board: you need to reposition and give him a little leeway in the process.
That's dangerous, as if the king escapes now you will have to start all over again and you could miss the 50 move deadline. If this happens, better offer a draw and analize the game with your opponent.
But if done correctly the king cannot escape, will be forced back into the corner of doom; and at the very end there is usually more than one way to actually mate. One is shown in this game.