Right and wrong bishops
The h-pawn promotes on h8, a dark square. White's bishop moves on light squares, so it can never control h8. This is the wrong-coloured bishop.
If the black king reaches h8, White cannot drive it out. The bishop can take g8 and h7 away, but never h8 itself, and the attempts end in stalemate. With a dark-squared bishop the same position is a win: put the bishop on c3 instead of d3 and every black move loses.
Racing for the corner
In this position Ke6 and Ke7 both draw. Moves that waste time, such as Kd7 or Kc6, lose.
Stay precise on the way. In the demonstration line, after h5 only Kg7 and Kf7 draw, while Ke6 and Ke7 lose. Once the king is in the corner, keep it there.
The stalemate finish
With the black king on h8, the white king on g6 and the bishop covering g8, pushing the pawn to h6 leaves Black with no legal move. White cannot make progress without allowing stalemate, so the game is drawn.
Remember
- The bishop cannot cover the corner
- Race your king to h8
- Stay in the corner
- Stalemate saves you