1) The best place to be is immediately in front of the white pawn, stopping it from advancing.
2) If you have to step back from the best place, step straight back along the same file as the pawn.
3) If the white king moves next to its pawn, on the adjacent file and same rank as its pawn, take the opposition.
Let's see these tips in action.
You are already in the ideal spot in the starting position. That is, as in 1) above, you are right in front of the pawn on its file. So you go on to 2), which is stepping straight back. By moving straight back to e7, you plan to stop white’s king from controlling the crucial squares in front of the white pawn. If white moves to f5, you move to f7. Then the white king would not be able to go forward to e6, f6, or g6.
In the diagram above, White chose to move his king to d5 and you stepped opposite him to d7, thus controlling e6, d6, and c6. The control you took is called the “opposition.” Because you had the opposition, white had to either retreat his king (in which case you would move in front of his pawn again) or push his pawn with check, which he did in the diagram above. By the end of the diagram above, we have a familiar position. It is the same position as in our first diagram, just moved one rank forward. And, guess what, we use the same three steps to draw the game.
The final position is a stalemate, where you are not in check but have no legal moves. By definition, stalemate is a draw. There are a couple other ways this endgame might have resulted in a draw. If white never pushes his pawn, and just moves his king around, you will be able to claim a draw by three-time-repetition of position or by the 50-move rule (50 moves without a pawn move or capture). White might also draw by allowing you to capture his pawn. If that opportunity ever happens, be sure to grab that pawn.
It's time for a quiz to make sure you understand the best place for your king. Hint: Remember 1) at the beginning of the article.