Every fingering that fits a hand
2110
open
211x
easy
2114
moderate
2554
moderate
x998
easy
What is true of it
Aaug is A, C♯ and E♯ — 1, 3 and #5 counted from A.
The easiest of the 5 fingerings below is 2110: 3 fingers, held at the 1st fret.
1 of them use open strings, which is what makes a shape quiet to change to.
Where its notes are on the neck
The brass dots are A, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
Aaug/C♯
x110
Aaug/E♯
x554
An inversion is the same chord with a different note lowest. The name changes to a slash name because the bass is what a listener hears as the foundation.