The two bishop mate is a simple mate. It does contain the possibility of a stalemate, so make sure your opponent has a place to move if your is not delivering a check. The easiest path to mate is to push your opponent's king into a corner. To do this have your bishops covering the diagonals that are side by side, so your opponent's king can't crossover. Then use your king to push the other king into a corner. The bishops squeeze in tighter and tighter and eventually your opponent is cornered. It gets trickier here. Intially your opponent cant attack the bishops because they can eaisly move away and maintain their diagonal but as the King becomes more and more cornered the flight squares for the bishops become smaller. The trick is to sheperd your opponent in while moving your King forward whenever your opponents king moves back. Find the point were your king has almost (not totally or its a stalemate) closed off the Kings flight squares and then transition your bishop(the one that is the same color as the corner square) from its guarding role and into attacker that will deliver the mate. Your King will be the one that is forward cutting off two squares, keep this in mind. If you go over it a couple times it becomes clear. The mate looks like this.

 --- --- --- ---
|   |   |   |BK |
 --- --- --- ---
|   |   |   |   |
 --- --- --- ---
| WB| WB|WK |   |
 --- --- --- ---
|   |   |   |   |
 --- --- --- ---  
Most people think that the only way to mate with two bishops is by driving your opponents king into the corner, its not. The other much more difficult(to me at least) way is to drive the King against the edge and deliver a mate like this.
 --- --- --- ---
|   | BK|   |   |
 --- --- --- ---
|   | WB|   |   |
 --- --- --- ---
|   | WK|   | WB|
 --- --- --- ---
|   |   |   |   |
 --- --- --- ---  

Two Bishops and a King vs. King - Endgame

See also: chess notation.

This sounds and looks like a tricky situation, but it's actually quite easy to mate you opponent.

The first step in the process of mate is to place your bishops side by side. The motive behind this is to enclose and restrict the opponent's king in a "pyramidal tomb". He cannot cross the diagonals of which the bishops cover, nor can he advance and attack the two bishops. The positioning should look something like this:
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 8
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 7 
+---+---+---+---+---+---+---+---+
|   |   |   |   |BK |   |   |   | 6
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 5
+---+---+---+---+---+---+---+---+
|   |   |   |WB |WB |   |   |   | 4
+---+---+---+---+---+---+---+---+
|   |WK |   |   |   |   |   |   | 3
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 2
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 1
+---+---+---+---+---+---+---+---+
  A   B   C   D   E   F   G   H

The second step in this process is to push the black king backwards onto the back rank. How do you do that, you ask? Well, the key to pushing the black king backwards is to have the bishops zig-zag one square at a time towards the black king, all while the white king gives support. The king is going to be a protection piece, so you must bring him up so he sits right next to the bishop. It doesn't matter which side, but for this example I'm assuming the king is to the left. Now, whichever side your white king is on, you are going to move the opposite side bishop up one square, towards the white king (to the left, in this case). This is how it should be done:

1. Kc4 Kd6 - White's king will give protection to the bishop soon to be moving on d5.
2. Bd5 Kd7 - White's bishop now forces black's king to be pushed back.
3. Be5 Ke7 - Bring the other bishop up so they can seal the pyramid.

We are now here:
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 8
+---+---+---+---+---+---+---+---+
|   |   |   |   |BK |   |   |   | 7 
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 6
+---+---+---+---+---+---+---+---+
|   |   |   |WB |WB |   |   |   | 5
+---+---+---+---+---+---+---+---+
|   |   |WK |   |   |   |   |   | 4
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 3
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 2
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 1
+---+---+---+---+---+---+---+---+
  A   B   C   D   E   F   G   H

We are going to continue to drive black's king back until he is on his back rank with only two spaces two move.

4. Kc5 Kd7 - Bring up white's king to protect the bishops.
5. Bd6 Kd8 - Push the black king back.
6. Be6 Ke8 - Bring the other bishop up.
7. Kc6 Kd8 - Bring up white's king.

The board should look like this:
+---+---+---+---+---+---+---+---+
|   |   |   |BK |   |   |   |   | 8
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 7 
+---+---+---+---+---+---+---+---+
|   |   |WK |WB |WB |   |   |   | 6
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 5
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 4
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 3
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 2
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 1
+---+---+---+---+---+---+---+---+
  A   B   C   D   E   F   G   H

The third step is to drive the black king in the corner. Remember that you must keep the black king on the back rank to keep him from getting away.

8. Bf7 Kc8 - White's move prevents black from moving to e8, thus forcing him leftwards into the corner.
9. Be7 Kb8 - Again, white prevents black from moving to d8, forcing him leftwards.
10. Kb6 Kc8 - This is an important move by the white king, as it prevents the black king from leaving the back rank.
+---+---+---+---+---+---+---+---+
|   |   |BK |   |   |   |   |   | 8
+---+---+---+---+---+---+---+---+
|   |   |   |   |WB |WB |   |   | 7 
+---+---+---+---+---+---+---+---+
|   |WK |   |   |   |   |   |   | 6
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 5
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 4
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 3
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 2
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 1
+---+---+---+---+---+---+---+---+
  A   B   C   D   E   F   G   H

Now it's time to bring your bishops down and force the king into the corner for the checkmate.

11. Be6+ Kb8 - White brings the bishop down from f7 to deliver check, thus forcing the black king to the corner.
12. Bd6+ Ka8 - Again, the bishop coming down to deliver check.
13. Bd5++ - Bring the bishop down again and deliver the checkmate.

It should look like this:
+---+---+---+---+---+---+---+---+
|BK |   |   |   |   |   |   |   | 8
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 7 
+---+---+---+---+---+---+---+---+
|   |WK |   |WB |   |   |   |   | 6
+---+---+---+---+---+---+---+---+
|   |   |   |WB |   |   |   |   | 5
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 4
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 3
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 2
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 1
+---+---+---+---+---+---+---+---+
  A   B   C   D   E   F   G   H

Remember!

There are 3 steps:

1 - Set your bishops up so they are side by side. Get the king next to the bishops.
2 - Drive the opponent's king to the back rank using a zig-zag motion with the bishops. Make sure the king supports the bishops!
3 - Force the opponent's king into the corner and make sure he doesn't leave the back rank!

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