In this relationship it is the bass note, or root of the chord on the A string that it the common note as you practice alternating.

Again, spot the A string and practice swapping between chords. 

Tip:

Different chord shapes tend to to suit different genres.  The more you familiarise yourself with timbre and quality of each chord, the more chance you have of using it effectively, whether you're composing, rehearsing, practicing or performing.

Study the relationship between the a chord shape and g chord shape