I am struggeling with this type of endgame position. We agreed on a draw, but can anyone tell me how I should have proceded or how I could have avoided this draw position?

Who's turn is it to move? If it is black's turn to move his king can just mirror your king and force a draw. There is no other option for black.

If white is to move if he moves Kd3 then you move Kb4 and I believe you will get the a4 pawn and be able to promote.

If white moves Kb3 then you move Kd4, he'll stay around there to eventually take your a pawn with something like Ka3, you'll move to take his h and g pawn and it looks like you'd queen at the same time. Someone better than me would have to say if you could turn that into a win with your extra pawns.

Blacks position is far superior here. This would be extremely difficult for white to win, and easy - but time consuming for black. White cannot move to h3 or h4 because of the pawn on g4. He cannot move his King to b4 or c4, so he can't protect that pawn on a4 for very long. 

Here:

42. Kd3 Kb4 43. Kd4 Kxa4 44. Ke5 Kb3 45. Kf6 a4 46. Kxg6 a3 47. Kxf5 a2 48. Kxg4 a1=Q 49. h4 Qg7+ 50. Kf3 Qg6 51. Kg2 Qe4+ 52. Kf2 Kc3 53. f5 Qxf5+ 54. Ke3 Qg4 55. h5 Qxg3+ 56. Ke4 Qg5 57. h6 Qxh6 58. Ke5 Kc4 59. Ke4 Qg5 60. Kf3 Kd3 61. Kf2 Qg4 62. Kf1 Qf3+ 63. Kg1 Ke3 64. Kh2 Qd5 65. Kg3 Qg5+ 66. Kh3 Kf4 67. Kh2 Qd5 68. Kg1 Ke3 69. Kh2 Kf3 70. Kg1 Qg5+ 71. Kf1 Qc1# 

I believe Black simply wins here.

If 42.Kd3, DaneHitchins has got it right. And if 42.Kb3 Kd4! and White will get squeezed of the a-pawn and Black wins easily

triangulation wins again!

Ah yeah that is better than what I suggested, simply forcing the king away from the a pawn if he goes Kb3.

Overall a good draw offer by white as it was the only way to save the game.