The Two Bishops
Checkmate can always be forced with king and major piece against lone king. Checkmate can never even come about with king and minor piece against lone king. But with king and two minor pieces against lone king, the situation is more complicated. The plan in all the basic positions involving two minor pieces and king against king is to drive the lone king into a corner of the board. Getting him to the edge just isn't enough.
The Checkmate
The easiest checkmate to get with king and two minor pieces versus lone king is the one in which your two minor pieces are both bishops. Here you can checkmate the lone king in any corner of the board. The checkmates look like this:
The e5-bishop delivers the check and covers g7. The d5-bishop takes away g8. The king takes away g7 and h7.
The plan in these endings is basically simple. Step 1 is to drive the lone king to the corner with the use of both your bishops and your king to methodically take squares away from him. Step 2 is to make sure your bishops have enough room to operate. Step 3 is to get your king out of their way at the last minute.
Working It Out
Although the concept is simple enough, it is very tricky to use the three pieces together as a team. The bishop's power is more subtle than that of the major pieces. Just try to checkmate a lone king using two bishops like you did with two rooks, and you will soon see that it can't be done. So we will look at a checkmate using two bishops and king versus king and work it out, move by move, to understand how it was done.
White to move. 1. Bf4. Notice that the fifth rank is off limits to the lone king, thanks to the bishops. 1…. Ke6 2. Kd4.
The strong king comes up to help. Notice that d6 is off limits to Black. 2…. Kd7 3. Kd5. Now the sixth rank and c7 are off limits. 3…. Ke7 4. Be5.
The f6-escape square is taken away. 4…. Kd7 5. Bf5+. Now much of the seventh rank is denied Black. 5…. Ke7 6. Kc6.
The bishops are perfectly placed, so White now brings his king closer. 6…. Kf7 7. Kd7 Kg8.
Alert! The Black king can only move to f7 or f8. Therefore White will blow it by moving 8. Ke8 or 8. Ke7, both of which produce stalemate. 8. Ke6. Now Black has a square to go to: f8. 8…. Kf8 9. Bg6. White takes e8 away. 9…. Kg8.
This is another alert. The Black king has only f8 as an escape. Therefore, White must avoid 10. Ke7 stalemate. 10. Kf6 Kf8. If Black plays 10…. Kh8 we end it early with 11. Kf7 checkmate.
11. Bd6+ White drives the lone king to the corner. 11…. Kg8 12. Be4. White gives himself some breathing room while not allowing the Black king out of his box. 12…. Kh8.
13. Kg6. The White king makes room for the bishops. 13…. Kg8 14. Bd5+ Kh8.
15. Be5 checkmate.
Learning these king and two minor pieces versus king checkmates is a very good course in learning basic chess strategy. All the principles you have learned and will learn in the future apply: Control the center, coordinate your pieces, use all the pieces, and make use of threats. Once you know these basic checkmates by heart, you will probably already be a pretty good chess player.

