http://www.chess.com/blog/NimzoRoy/k--p-vs-k-endgames
King/Pawn Checkmate
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Your specific ending was an automatic draw.
Normally K+P vs. K depends on the position of the kings, and it's a bit tricky to learn but I would definitely reccommend it as a starting point to improve your chess.
However your game had a side pawn, which is nearly always a dead draw.
Could someone give solution/advice. I had white. I had a King and pawn remaining on the board. My opponent had just a King. How do I check mate? I thought you were supposed to lead with the King down the board and let the pawn catch up. I hope this is not an automatic draw?
Thanks in advance all.