I call the endgame king+bishop+knight vs. a lonely king an 'embarrassing' endgame because I know too many cases where chess players left a chess board embarrassed. Indeed, just imagine how would you feel if you had a theoretically winning endgame, huge material advantage and yet the game was a draw! Surprisingly it happened to many strong chess players. One of the most recent high-profile cases is the game of then women world champion Anna Ushenina.
Funny, but Ushenina's opponent already had this endgame in one of her games. She was the stronger side in that case and showed an impeccable technique:
So, as you could see, Olga Girya has proved that if you know the correct technique, it is not that difficult to win this endgame. As a matter of fact, some chess players might say that they would checkmate the opponent with their eyes closed. Actually, this is exactly what happened in the next game where Judit Polgar checkmated her opponent in a blindfold game!
I anticipate your question if this endgame happens only in women's games since so far we have analyzed only games played by ladies. Of course male grandmasters had their share of embarrassment as well. GM Vladimir Epishin was Anatoly Karpov's second and one of the leading grandmasters in the world in the mid-90s. Yet, he failed to win this endgame in the next game:
As you could see, a very strong GM wasn't even close to winning this endgame and at the point when he stalemated his opponent, the game would be claimed a draw due to the 50-move rule anyway. What went wrong there?
Apparently Black didn't know the correct technique and it is very difficult to find it on your own when you are tired after a long game and probably very short on time. Meanwhile, the correct procedure is relatively easy and can be split into three parts:
Push your opponent's king to the corner of the board (the easy part).
If the corner is 'wrong' (that is the bishop cannot control it), force your opponent's king to the right corner. (This is the most difficult part of the whole plan)
Checkmate the king (the simplest part).
Watch how a super GM does the most difficult part:
Here is another very strong GM making it look very easy:
There is one trick which you must know. When you push your opponent's king from the 'wrong' corner to the 'right' corner at some point it looks like he just escapes. But this is just an illusion. The knight and the bishop create a firm barrier, so the king is still locked. The next diagram shows this important approach:
In the next game Black resigned when his opponent was about to demonstrate this trick:
And here is one more example of this very important and useful pattern:
So, the endgame is not that difficult to master yet it is very tricky. I recommend you to play a couple of training games in this endgame with your friends to assure that if you ever encounter this endgame, you will leave the board smiling.