There's no real "punishment" to opening moves like this. Most probably, with best play, it would lead to a draw - it's just supposedly easier than other openings for black. It simply gives almost guaranteed equality. I would just play a reversed d4 (i.e. 1...d5), with black having already played h5.
How do you punish 1.h4

Well i don't think you should want to punish this immediately. Just enjoy the free tempo and the fact that white has weakened his kingside very early on. I would probably not play 2...Nc6 and try to get a bigger center with 2...Nf6 and later on c6 and d5. The h4 move will prove to be weak at a later stage. Just play whatever you play as white vs e4 e5 though.

Like Hyupocrism said, there is no punishment, it just yields equality pretty much instantly. It's still very much a game of chess.

One idea is to not lock up the center as in an open game that flank space/pressure won't mean nearly as much.
Another is to keep an eye out on the g4 square and maybe use it for your own action on the kingside in the future.
But after the very first move (1.h4) you can't make plans of Bg4 to pin a knight that isn't there yet :)
Even though the first move was uncommon, the character of the game will depend much more on the next few move by bother players.

I know the basic principles ,play e5,d5 and develop your pieces but how would you best punish h4? Just for fun I am wondering. Here is my stupid line.