Two Bishop Mate is another checkmate which seems problematic for club level chess players to implement, even though it should not be.  I have previously written about Knight + Bishop Checkmate, which is much more subtle, but no doubt very important to know.  The main idea of checkmating with two bishops is occupying the center with the bishops,

using the King to force the opponent’s King to the edge of the board and checkmating.

We still have 50 move rule, but it’s less crucial in Two Bishop Endgame since checkmate is being forced much quicker than in Bishop + Knight or Queen vs. Rook cases.

I will explain step by step how exactly to checkmate alone King with two Bishops.

Step 1

The first step in the Two Bishop endgame is to occupy the central squares d4, d4, e4, e5 with our Bishops. We need to first get to the position shown on the diagram below, placing the Bishops on the long diagonals h1-a8 and a1-h8.  Than we place our Bishops on e4 and d5 squares limiting the Black King to only 12 squares (see the actual game below).

Step 2

In this step we walk our King to the f5 square and to getting ready to shift our bishops to c5 and d5. We need to move the Bishops so that Black’s King cannot attack any of the Bishops. So, we first shift dark square Bishop to c5 and only then shift light square bishop to d5 (note how two bishops guard each other creating the wall and making it impossible for Black King to penetrate).

Step 3

At this point we have achieved the position shown on the diagram below. Now we need to transfer our King to e6 and to shift the Bishop once again to the left occupying b6 and c6. Remmember that we need  not let Black’s King to attack our Bishops.

Step 4

At this point the Black King has only two squares to move on: a8 and b8. We checkmate the Black’s King the following way: play 19. Bd7 to trap the Black King in the corner and then after 19… Ka8 we play 20. Bd4 followed by 20…Kb8 21.Be5+ Ka8 and finally 21. Bc6#

We have forced a checkmate with Two Bishops in 21 moves. Remember the basic points while checkmating with two bishops:

• Occupy the center with Two Bishops, in particular e4, e5, d4, d5
  

• Transfer your King to f5
  

• Shift your bishops to the left, forcing the Black King to the edge of the board

• Move your King a6 and checkmate the Black's king with the bishops 

If you want to be able to reproduce the mating pattern in tournament conditions you need to practice this endgame against a human opponent or a computer: "practice makes perfect". If you're interested in learning more endgames I recommend to taking a look at Improve Your Endgame Play and 13 Checkmates You Must Know which covers stadard mating patterns.