just develop normally until you find a way to break open some lines. remember pawns can not go backwards, so while a pawn move may be good(or even winning) it MUST also create a weakness.
What to do if the opponent does a lot of pawn moves
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Yes, what he said. Develop your pieces and watch for any weakness in his pawn structure, even if it's only temporary. Then exploit that weakness.
anticipation is the Name of the game, when your opponent doesn't develop and storms your position. sometimes the idea is to bind all the pawns up, locking pawn after pawn- and knowing when and where he must take...
other times he might become loose and fail to protect them. Knights are superior warriors when it comes to hunting pawns. but hunt wisely... any peice including a knight can easily get stuck with no hops back to safety; so you must calculate carefully.
the rule is if you can grab a pawn without giving your opponent a tactical or strategic gift, do so, then come right back. even if it means going back to the very same square
Apr 2, 2015
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#5
I think that Morphy -- Meek, American Congress 1857 is instructive: http://chessskill.blogspot.com/2015/02/flexibility.html
This type of behavior used to intimidate me too. But, now, because I've learned to do the things listed above, when someone does this, I just smile and know they are only improving my chances of winning. 
I would also add that once your more comfortable handling the dubious early pawn storm, you could consider gambiting a pawn opening the game to take advantage of your lead in development. Kleelof is right, be happy when your opponent does this it's highly frowned upon.
I'm rated only 800.
Recently I met an opponent who kept moving a lot of pawns from the opening. It seems against the common practice or general opening advices, but I have no ideas how to response, and could only develop my pieces as usual. Soon his intimidating pawns seemed unstoppable while I could hardly find a safe place for my piece to go. No wonder I lost a game or two to him.