So, I'm white and I reach the position below, which is a win for white with correct play and a loss for white with incorrect play. The idea is to block the KS pawns so that after there are no more pawn moves black has the move. Now, while this does not require extensive calculation, is there position a matter of sheer calculation, or are there pawn patterns and ideas I should know that would help me find the correct moves?

copy opponents pawn moves ex: h6 h3 g5 g4 etc...

Eek, what a position!  You say this is a win for White with correct play (as though you are certain that is the case)...if so, post some vars.  I'd like to see it!

Obviously calculation is going to play a role but I think the key to winning an endgame like this is to first realize that the position is fundamentally a Trebuchet position (i.e. both kings in front of their respective pawns). 

By reducing endgames down to basic elements it's often possible to find order in chaotic positions.  Once you make the connection that this is a Trebuchet position, you realize if the kingside pawns didn't exist, the side to move would lose the game.  To put it another way, the side that makes the last pawn move wins due to reciprocal zugzwang.  Armed with that information, calculating the pawn moves necessary to place black in zugzwang is relatively straightforward. 

As previously mentioned, g4 is one of the winning moves but it's not the only one.  Both f3 and h3 also win while h4 and g3 lose.  It looks like f4 draws because even though black wins the opposition and captures b5, the white king has time to clear a path for the f-pawn and secure a queen...just in time to avoid losing.

Here are a few examples:

Zounds, I am messed with! (but come on, two double-exclam first moves?!--you're getting punctuation-happy).

I did get a little carried away, didn't I?

So what you are saying Gonnosuke is that the only idea you need hear is that of Zugswang, and after working that out you just need to calculate the moves?

NM Tonydal, this position is one of chess.coms very own puzzles, and while it is certainly possible I misunderstood the puzzle, I'd be more than happy if you could provide variations where black wins or draws. After all, the purpose of this post is for me (and others) to try and understand the position. So, not only would I appreciate it if you could find other results, I'd actually encourage it :D.

Isn't recognizing zugzwang half the battle?  If you don't see it coming, you won't play it correctly so knowing how to identify zugzwang is a huge part of the equation.

You asked if there are patterns that will help you find the right move which is why I mentioned the Trebuchet position.  If you recognize the Trebuchet, then you have a blueprint for handling the kingside pawns since you know that the player who makes the last pawn move will win the game.  Any sequence of pawn moves that results in you making the last pawn move wins.  I assumed it was that kind of pattern that you were referring to when you asked for ideas on how to navigate this type of position.

Perfect! Thank you Gonnosuke. I will look up the Trebuchet position :D

No need to look it up, that pawn and king configuration *is* the Trebuchet position. You can verify quite easily for yourself that whichever side's king has to move loses, as it can no longer defend its pawn.

Gonnosuke, by "patterns" I think the OP meant patterns on how to force zugswang with the kingside pawns, rather than simply recognizing the king/pawn "Trebuchet" pattern on the queenside.

"The idea is to block the KS pawns so that after there are no more pawn moves black has the move. Now, while this does not require extensive calculation, is there position a matter of sheer calculation, or are there pawn patterns and ideas I should know that would help me find the correct moves?"

Yes, that's how I read it also, Suker.

Run a computer on it. g4 wins.

This is correct play if it is Blacks move.  White to move plays 1.g4.  The wild thing about the position is that White will win because he will queen with check in both best play variations.

Knowing what wins is far less important than knowing why -- and how -- this type of position is won.  I'm guessing that the ability to win positions like this OTB would give Class players an advantage over most of the competition.

If you run into the following position a week from now while playing in an OTB tournament, knowing that g4 wins the OP's position isn't going to be very useful.

in your position,f3 wins,right?

No, 1.f3 loses to 1...f4 since it allows black to make the last pawn move and puts white in zugzwang, forcing him to move his king or allow black a passed pawn.  Both options give black the win as you can see below.  See the first variation for the correct move, 1.f4!.

When the kings are in a full-point mutual zugzwang position as they are here, the first side to exhaust all available pawn moves -- without allowing the enemy to create a passed pawn -- wins the game.

Very nice position and  very nice further explanation by Gonnosuke. From the OP you need to know what was well explained in the earlier posts. Clearly people use silicon beasts to find answers but never learn why the moves suggested wins. Probably one of the best and most informative posts on chess.com in a long time. Of course it is not as popular as the normal "What's the best opening."

Wow! A thread that actually has useful, accurate information (aside from the usual drivel from tonydal). It almost makes me think that paying $100 is worth it.

This is definitely a practical study.  There was something I didn't get in secrets of pawn endings about this exact subject.  When I get a chance to post it maybe I can get a better explanation.