What is true of it
Aadd9 is A, C♯, E and B — 1, 3, 5 and 9 counted from A.
On an instrument that cannot reach all 4, the 5 goes first, in that order.
The easiest of the 1 fingering below is 2102: 3 fingers, held at the 1st fret.
All 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
Aadd9/C♯
6470
Aadd9/E
9b9c
Aadd9/B
4100
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.