How to win pawn vs pawn?

Exactly what I did.

ok, I'm confused. Isn't this a tablebase draw?

looks drawn.  his analysis shows white blundered a king move (admittedly this is tricky to do 100% accurately under time pressure) and went from 0.0 to -48 (is it on drugs? its like M10 or less) and game over.  While the computer can draw it, play these things out, someone will choke and lose most often if there is any time pressure. 

This position looks like a draw, but you can play for your opponent's blunder

The post doesn't say who was on move so I was analyzing

1 Kg5 Kg7 2 g3 Kf7 3 Kh6 Kf6 4 g4 g5 5 Kh5 Kf7 (only move) 6 Kxg5 Kg7 and the normal maintain-the opposition until the pawn is pushed to g5 and you concentrate on putting your king on g6 or g7 or maintaining the opposition.

If black plays 2 ... Kh7 then just swap h for f in moves 3 and 5.  If Black mis-analyzes and thinks there is another stalemate option there is the deceptive  2 g3 Kh7 3 Kf6 Kh6 4 g4 g5 5 Kf5 Kg7(?!)  6 Kxg5 Kh7 7 Kf6 Kh8 8 Kg6 Kg8 9 g5 Kh8 10 Kf6(?) Kh7 11 Kf7 Kh8 (note 12 g6 is stalemate) 12 Kf6 Kh7 13 g6+ Kh8 (14 Kf7 is stalemate) 14 g7+ Kg8 15 Kg6 stalemate.  However White prevails with 10 Kf7 Kh7 11 g6+ Kh8 12 g7+ Kh7 13 g8=Q+

With the Black pawn still on g6, Kf6 is met by ... Kh6 if the White pawn is on g3 and by ... g5 if the White pawn is on g4.  The key is to force a White capture on g5 after the White pawn is on g4 and when Black can still get the opposition on g7.  Letting White capture on g6 would be a loss for Black even if the Black can can the opposition and the White pawn is already on g5.

ok.. this analysis is head spinning

King and pawn endings can be more difficult than they might seem at first.

No, it's a draw. 1.Kg5 Kg7 2.g3 Kg7 3.g4 Kf7 4.Kh6 g5! 5.Kxg5 Kg7 Black has the opposition, so therefore it is equal. I'd highly recommend Van Perlo's Endgame Tactics.

1...Kg7 2...Kg7 is a bit illegal but it's Black to play according to the FEN so that brings it back into sync (not that it matters who is to play - it's drawn whatever). If it's PvP on the same file, one king is on the same file between the pawns and the other protects his pawn it's a draw whoever moves (see e.g. Averbakh Pawn Endings Position 46 Pergamon Press version, with both pawns on their starting rank). 

Really quite easy to draw for either side I think. Just avoid getting you king level with or behind the opponent's pawn (when it would be just possible to lose). For Black play g5 if and when White plays g4 and make sure you can play Kg7 if White takes your pawn (White can play either 2.KxP on 1...g5 otherwise 2.Kf3 followed by 3.g3 or 3.g4 as appropriate and do the same). E.g.

(Played at about 1 sec per move.)