What's the plan against Black's kingside fianchetto when playing Queen's pawn game? I often play 1. d4. In many of the variations that arise, Black decides to castle kingside with the bishop fianchetto. 

I do not know what the general plan is in this case. Normally without the fianchetto I would play f4-f5, some kind of Marshall plan or Stonewall formation with the Knight. But when there is a fianchetto I do not know what to play for.

I know the question is vague. But I am looking for strategies from different players with different styles. What to do with a kingside fianchetto when playing 1.d4 and also castling kingside?
You can still play a Stonewall Attack when Black decides to castle kingside with the bishop fianchetto.

Black reacts with d5

Here is an example with "normal" moves from Black. 

[FEN ""]

1. d4 Nf6 2. e3 g6 3. Bd3 Bg7 4. f4 d5 5.Nf3 c5 6. c3 O-O 7. O-O Nc6


The stonewall attack is a solid opening with grip in the center: 


White controls the important central squares (d4, and e5) 
White can install a knight in e5 which will force Black to weaken its position if it wants to remove it.
White can play this typical manoeuvre to exchange the bad bishop in
c1 against the knight in f6 by playing Bc1-d2-e1-h4.
With a closed center, White can then expand on the king's side with g4...


Here is an example with black normal moves that are a bit cooperative!

[FEN ""]

1. d4 Nf6 2. e3 g6 3. Bd3 Bg7 4. f4 d5 5. Nf3 c5 6. c3 O-O 7. O-O Nc6 8. Bd2 b6 9. Be1 Bb7 10. Bh4 e6 11. Nbd2 Ne7 12. Bxf6 Bxf6 13. g4


Black reacts with d6

The setup with d6 suggested by @user1583209 is very clever. d6 is a flexible move that allows Black to counter-attack with e5. Here is an example where Black is okay:

[FEN ""]

1. d4 Nf6 2. e3 g6 3. Bd3 Bg7 4. f4 d6 5. Nf3 O-O 6. O-O Nc6 7. c3 e5


I would suggest reacting with 7.e4 instead of 7.c3 like in this game (obtained by transposition)

[Title "Gleizerov, Evgeny (2544) vs Das, Arghyadip (2404), Gurgon Op. 2009"]

[FEN ""]
1. f4 g6 2. Nf3 Bg7 3. d4 Nf6 4. e3 O-O 5. Bd3 d6 6. O-O Nc6 7. e4 e5 8. d5 Nb4 9. fxe5 dxe5 10. Be3 b6 11. Nc3 Ng4 12. Bg5 Qd6 13. Qe2 h6 14. Bd2 Nxd3 15. Qxd3 Bd7 16. h3 Nf6 17. Ne2 Ne8 18. c4 f5 19. Ng3 f4 20. Nh1 Nf6 21. Bc3 Rae8 22. Nf2 g5 23. a3 c5 24. dxc6 Qxd3 25. Nxd3 Bxc6 26. Ndxe5 Bxe4 27. Bb4 Bxf3 28. Bxf8 Bxg2 29. Bxg7 Kxg7 30. Kxg2 Rxe5 31. Rfe1 Rf5 32. b4 h5 33. Rac1 g4 34. hxg4 hxg4 35. c5 f3+ 36. Kf2 Nh5 37. c6 g3+ 38. Ke3 f2 39. Rf1 Rf8 40. c7 Rc8 41. Kf3 Kg6 42. Kg2 Kg5 43. Rfd1 Nf4+ 44. Kf3 Nh5 45. Rc4 Kg6 46. Kg2 Kg5 47. Rd5+ Kg6 48. Rc6+ 1-0