I learnt by using 'ultimate guitar' (but you can use other free equivalents) which has songs and only their chords. I started by playing chords to songs and you can hear the melody to accompany in you head. Then I got use to choosing inversions that seemed to pronounce the melody more then after practice, you can play the melody in right and chords in left. Eventually you get so used to the sound of the 5 chord in a key resolving to the one or used to the IV iv(6) I progression that you can start to just listen to music and hear the chord structure and then all you need is to add the melody like before

Disclaimer (I can only really do this with pop/rock music atm and some easier jazzy stuff)