What if someone's first move is a3

makes no sense

Play d5, I don't know.

They're just hypermoderning you. Play 1...a6 to hypermodern them back. 

This actually makes sense (for a given value of the word "sense").

After all, 1. a3 e5 can be met by 2. c4 and a reversed Sicilian with a tempo more; while 1. a3 d5 can be met by 2. Nf3 followed by a reversed Benko Gambit with a tempo more. In both lines, the 1. a3 move is useful.

But after 1. a3 a6, the shoe is on the other foot.

It's called Andersson's Opening. Basically it's whites way of saying he wants to be black. Also it opens up the queenside bishop along the a2 g8 diagonal and stops black from playing things like Ruy Lopez.

I've always found it difficult to get the c1 bishop to the a2 g8 diagonal.

God damn it. 

that language is way out of line!

Being a lower rated player like you and I. The best response is to take the center of the board. E4, D4, or even knight move. At our level its best to stick to good sound Chess.

I can't remember exactly but I remember reading it was essentially a waiting move by white.

 wait so you mean that the opponent is going to change their move according to your move? then what would be the best move without getting a piece cornered? 

Isn't hypermodern chess when the opponent starts with b3 or g3 followed by bb2 or bg2? I don't think it starts with a3

do you think the fried liver attack works this way?

 i'm pretty sure that a3 is part of the plan to counter a fried liver attack (along with your knights) so if you plan to do a fried liver so that is unlikely, unless your opponent makes a mistake

the andersons opening is a decent difficulty to counter, but one wrong move could get your important pieces wiped

http://www.chessgames.com/perl/chessgame?gid=1019039

http://www.chessgames.com/perl/chessgame?gid=1019043

http://www.chessgames.com/perl/chessgame?gid=1019048

dont underestimate 1 a3 ,, chess is a battle , a move like this may cause confusion dont let it ,

take your time imagine you was white how would you develop ? as pointed out that c1 bishop wants to go to b2 so either b3 or b4 is in your thinking as the next move

now be black again , you got anything on your side that questions either b4 or b3 ?

a3 a5 looks a fun way of going cmon then

If 1 a3, then play according to accepted principles like those in GM Evans, et al. classic How to Open a Chess Game.

Note that White has not thrown the game away - he/she has just given away the advantage of the first move for potentially the advantage of playing someone who doesn't understand opening principles and makes poor moves or falls for traps.

You should play to control the center, develop N's, control space as much as practical without making too many P moves, make threatening moves so White can't freely develop, and try to gain the initiative with the extra tempo W has given you.

Because you're seeing positions that are probably less familiar to you than to the White player, you need to make sure you overprotect pieces, don't leave any hanging and spend a little extra time looking for potential forks or pins of your pieces you can't handle.

if you play 1.a3 take a break from chess because you're mentally crushed