A G Augmented (Gaug) chord contains the notes G, B, D#. It is built from the augmented formula 1 - 3 - ♯5, with G as the root.
What chord should follow G augmented?
C major is the classic answer. The D♯ in Gaug sits one semitone below E, the third of C, so the voice leading is as smooth as it gets. E minor also works well for the same reason. What you generally want to avoid is stopping on Gaug — it's built to move.