I've recently begun studying openings, and I have a bit of a quandry. I can find a wealth of material on what moves to make against standard opening replies, but I don't see much about taking advantage of weak moves. Some options, like forks and such, are obvious, but I'm thinking of situations where the advantage is more subtle. Are there any resources that talk about what to do in your opening when your opponent gives you an opportunity?

These are positional advantages.

That is where BIG databases are handy. You not only get the good play, but also the bad, and hopefully what to do about it.

But sometimes you just got to wing it....

BTW, a big mistake, imo, is to try to punish a bad move. If you can figure out why it's bad, see if you can take advantage (more subtle than punish!) There is rarely a one move refutation.

I just simply make the right moves. If my opponent pushes a and h pawns, I takeover the center.

You lost that game not because he played a4, a5, a6, but because you hung two pieces in the opening.  If you hang pieces like that you can lose to basically anything.  The only thing his early pawn push did was waste time, and you correctly seized the center.  But you really needed to get castled kingside instead of moving the queen's knight.  Then he'd have had quite a foolish looking position.

read this:

http://www.chessville.com/instruction/instr_gen_play_v_patzers.htm

You completely ignored the one person who gave you the best possible advice. It doesn't matter if Kasparov gives you a 10-move variation that will gain a significant edge over White after 1.a4, if you hang two pieces before move 15 you're going to lose every time.

The OP's question vastly overestimates the importance of openings. An opponent playing a bad opening that doesn't lose material tactically is handing you a small advantage, nothing more.

 In his book Chess Openings: Theory and Practice, Horowitz had a concept of the "ideal variation".  In the ideal variation the opponent never made a move to stop the basic idea of the opening.  I found this concept very helpful in dealing with non-book moves.  I don't think this concept caught on. At least I know of no other books that uses this concept.  Nunn will occasionly use something similiar, he will give a variation where the opponent makes a pointless move (usually something like a6) to illustrate a threat.

The real killer with silly opening moves is the loss of time.  By making good opening moves you gain time to develop your attack while your opponent is wasting time shoring up self-inflicted weaknesses.

If your opponent deviates from a main line with a weak move, it creates a weakness in their position.  You will usually have to deviate from the mainline and be creative in order to take advantage of this weakness.  Don't just memorize lines without knowing their exact purpose!  If you know what move they should have played you can think to yourself, "what does the correct move accomplish on the board that this wrong one doesn't?".  If you can answer that question then you will be in good shape.

Excellent article, thanks!

My pleasure!

White can get away with playing moves like 1. h3  or a4 and often gets a psychological advantage if black thinks he must be able to punish white. Black should be able to equalize, but he certainly can't force a winning position. When I play against this stuff I just try to control the center and develop my pieces. If anything I'm more on guard and try not to overextend.

Its unfortunate but White can afford to waste time like this in the opening...As Hollywood said, White might not get an edge but there is NO way to refute any opening like this, or any FIRST opening move for white. For black its another story, moving 1....h6 might give him a miserable position but even then i don't think there is any "one move" refutation to these kinds of shenanigans. You just play classical and straight-foward and in the critical moment the enemy may sorely miss that one extra tempo he wasted in the opening.

The best way to "punish" bad opening moves is not to try to punish them at all, so much as to exploit the weakesses that they create in the opponent's position. The way to do this, of course, is to strengthen your own position by adhering to sound opening principles. I've learned by bitter experience not to try to "punish" an opponent that plays cockeyed opening moves. One can easily wind up tying onesself into knots and hanging pieces or making other mistakes that the opponent will then use to punish YOU.

To punish bad moves, you need to understand why the moves are bad. Answer the question yourself and you can find the answer yourself. Its necessary to understand theideas behind the opening to play the opening with any degree of success against the prepared and those who deviate.