If you are putting your Bishop on g2, you are not in a QGD, you are in a Catalan.
There are a number of routes that White can take. After 1.d4 d5 2.c4 e6, you have the following:
A) 3.Nf3 Nf6 4.g3, which is the Catalan. Now 4...dxc4 is the Open Catalan while 4...Be7 can lead to the Closed Catalan or a delayed Open Catalan where Black takes on move 6 on c4, or the flat out Closed Catalan, which is also what 4...c6 leads to.
B) 3.Nc3 Nf6 and now:
B1) 4.Nf3 is an old line that allows Black more options than he deserves. Today this move is not considered best, though it's by no means bad.
B2) 4.cxd5 exd5 5.Bg5 - This is known as the Exchange Variation. White has 3 strategies here. Minority Attack on the Queenside, Castle Queenside and go for a Kingside Pawn Storm, or develop the King's Knight to e2, play f3 and try to get in e4. This can lead to an IQP for White, Opposing IQPs, Hanging pawns for White, or an Advanced Center for White (e5 and d4).
B3) 4.Bf4 - White plays for control of the diagonal rather than going for a direct attack. I never played this move.
B4) 4.Bg5 - The main line. Now Black has various replies, like 4...Be7 or 4...Nbd7. The "main" main line is 4...Be7 5.e3 O-O 6.Nf3 Nbd7 7.Rc1 c6 and now both sides are trying to find effective moves without giving in. Black wants to wait to take on c4 until White has moved his Bishop. White would like to avoid moving his f1-Bishop until Black has taken so as not to lose a tempo.
I play Queen's Gambit often but I still often find myself unsure of when to exchange the c pawn. My tendency is to leave it there for along enough that black finally takes it and I can play a quick e4. But sometimes I don't get adequate compensation doing that (my bishop is usually on g2 at this point, so I usually don't bother trying to pick up black's pawn after it ...dxc4). The other main option is to exchange it earlier, but also I've seen it pushed a few times, and sometimes white can play Qa4+ followed by Qxc4 to pick up black's pawn, or even sometimes Ne5-Nxc4. I'm just wondering if anyone has any guidelines or thoughts about when to do something with the c4 pawn.