I was playing Queen's Gambit Accepted. How should I continue after 3. e3 c6? I had no idea what to do after that.
1.d4 d5 2.c4 dxc4 3.e3 c6
The simplest reply for white is Bxc4 which gives white exactly what he wants, a central pawn majority with tempo because he got his d4 pawn in the center plus his bishop on C4 while black basically doesn't have any pieces or pawns off their starting squares.
That said, a4 is probably also a good move as it makes b5 difficult for black.
Note that c6 isn't a great move for black because quite often in other lines he wants to move his c pawn straight to c5. If he ends up later playing c6-c5 then he has taken two moves instead of one to get there. Better for black would be e5, aggressively challenging white in the center or Nf6 fighting for the d5 and e4 squares.
A lot of players new to the QGA like to try to hang on to the pawn at c4 or build up a quick and big Queenside pawn storm, but it is an unstable and fairly neglectful strategy. Here, it looks like Black will follow 4. Bxc4 with ...b5 to kick away the bishop and start moving pawns forward; however, as @overtheboard suggests, if White keeps to solid chess principles (develop, don't overextend right away, castle, etc.), he or she will enjoy the better position. The QGA is classically played by Black by developing and attempting to undermine the center, not storm across the Queenside without developing pieces.
You can play an immediate 3. e4, and this might be a matter of taste, but that leaves you a bit vulnerable after 3...e5. I play the Classical QGA (1. d4 d5 2.c4 dxc5 3. Nf3 Nf6 4.e3), which uses e3 because it is the safest and more direct route to recapturing the pawn and completing development.
Why not play the move 3. e4 instead of 3. e3? that move helps you start staking a claim for the center and you get to recapture on c4, Win-Win. Unless black decides to protect the c4 pawn which is usually not advised