Why the bishops never meet
White's bishop moves on light squares and Black's on dark squares. They can never attack each other, and neither can contest the squares the other controls. That makes blockades very hard to break.
The fortress
Black's king stands on d6, in front of the d-pawn and on a dark square, so the white bishop can never check it or drive it away. The e-pawn needs to reach e5, another dark square, which the king and the bishop on the long diagonal both control.
If White pushes e5, Black simply takes the pawn. Otherwise Black's bishop shuffles along the long diagonal, and White has no way to make progress.
Typical mistakes
The king must hold its post. In the starting position Kc7, Kd7 and Ke7 all lose: once the king leaves d6, the d-pawn can move on.
Most bishop waiting moves are fine, since the king on d6 also covers e5. Just keep the bishop out of reach of the white king: after Kf5, for example, Bf6 loses the bishop to Kxf6.
Opposite-coloured bishops do not draw every time. Pawns far apart, which the king and bishop cannot cover together, can still win.
Remember
- Bishops on opposite colours never meet
- Blockade on your bishop's colour
- Keep the king on d6
- Let the bishop wait on the long diagonal