I'm no expert but when working out a song by ear you are said to look out for guiding notes/chords to do this ( but no hard and fast rule here ,just common usage ) .
If identifying the root of a song as G as you have ........you would look for its relative majors and minor also .The relative major chords would be the forth and fifth chords of its key ..........but also more often than not the relative minor would be commonly used and that would be Em ( the relative sixth ) .
To become familiar with these keys and their numberings i used the circle of fifths ( a very good and small addition that can be cut out and put on the guitar for reference to look down on while working out songs by ear .
There was once a great thread on here for the circle of fifths but i thought a little in deapth and may put a newbie off using thinking it was too complicated for to use .
When in fact you dont even need to know the workings of it ..........you can just use it and see if it helps working out numberings for shords in a key .
If i'm getting above my station here please clip my wings
by the way you can get a simple graph of the circle of fifths anywhere on google ..........after relating the bones of a song with its root and relatives .....more often than not all you have to work out next is how they have been broken up or added to for getting the flavour of the music .