I regularly play the Sicilian defense and often get caught out by white marching his queen-side pawns down to disrupt my defensive pawn structure. How do I counter this?

My opinion of the sicilian is that its typically a race to see who can get there attack (typically accompanied by a pawn storm) off first.  This is where time gaining moves and pressing early for the initiative becomes so critical, because whoever gets their attack off first has the advantage.  That being said, I always prefer playing the white side of this opening because I find it much easier to pawn-storm before your oppenent.  So, in my opinion, the issue isn't so much in dealing with white marching his pawns at  your king so much as it is about you marching yours towards his (or hers).

I'm sure someone else can explain it better, if I find a good example I'll post it here later.

march your a b pawns faster than he can his g h pawns

also sometimes you can use your oppenets pawns to sheild your own king

I presume the only way marching my a, b + c pawns will work is if white has castled on the queen side... Which plenty of players rarely do...

Can you post a game so we can see what's going on?  Any advice offered without first seeing the game would be pretty useless.

Here you go Gonnosuke. A game where the pawn advance brought me undone, even when I was actively trying to defend against it (though admittedly not adhering to jlaix's advice of attacking first):