King and Pawn partnership

that works only with King and pawn v.s King, The king travelswith the pawn to make a queen

its a basic strategy, but I prefer to start with  1.f4  then 2.Kd3

you saves 1 move 

Black played very poorly in this example. 3. ... Kh5 is a losing move while 3. ... Kf5 would have drawn.

Knowing how to win and draw king and pawn endings is important as they can come up often. Sometimes it is a win to have an extra pawn and sometimes it is only a draw, you can't count on your opponent to play as poorly as black did here. Instead of pushing the pawn first, white should try to get the king out in front of the pawn.

exactly

Jeremy Silman gives an excellent explanation on "Opposition" in his book "How to Reassess your Chess". It deals with King and pawn endgames and the strategy on how to win won positions, and how to draw drawn positions.

Highly recommended reading... as it is extremely important to understand these endgame techniques...

I'm actually struggling to fully grasp the concept...

> its a basic strategy, but I prefer to start with  1.f4  then 2.Kd3

Both 1.f3 and 1.f4 blow the win.  Like Loomis said, the correct strategy is to bring the king in front of the pawn... ie 1.Ke3 or 1.Kf3.