How to play against 1.a3?

Its actually a big dilemma.

If I respond 1...e5, they play 2.c4! And now they are an important tempo up in the Sicilian.  Which is clearly a bad idea.

If I respond 1...d5, they can play 2.d4!  Now I can't play a Queens Gambit because white has the option b4 available.

So basically, what opening should I try to steer the game towards where a3 isn't a useful move?

Someone hasnt been going to the troll school for a long time...

Going into a KID setup is pretty good since the move a3 is not useful when Black hasn't provoked it.

1. ... e5 is absolutely fine. Black can play solidly and get an equal game in all variations that white may choose. However, some consider that, since 1.a3 threatens b4, then black's most logical move should be 1. ...g6.

a3 is a bad move so i would play the four move checkmate

What big dilemma? Just develop your pieces and use common sense. 

By now you should know that some chess.com users lack common sense.

Take the center and crush your opponent.

Not always true - Since I play the Samisch, black has the pretty good option of the "Byrne System", basically playing a6 (or a3 in this case), c6, b5, etc.  So in this scenario he would be a tempo up. 

I wonder if 1...a6! is the best move. Now, if white plays 2.e4, he is unable to play many openings he would have otherwise wanted to, including Ruy Lopez, Italian (because a later Bb5 or Nb5 is unavailable, etc.)

people make these moves to avoid the mechanical responses of opening explorers. and force games from general principles. at a guess.

people make these moves to avoid the mechanical responses of opening explorers. and force games from general principles. at a guess.