What is true of it
A♭add9 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 1041: 3 fingers, held at the 1st fret.
None of them uses an open string, so this chord moves up the neck unchanged — the same shape 1 fret higher is the chord a semitone above.
It leaves out the 5. 4 strings cannot carry 4 notes, and the 5 is the one this chord can lose without changing what it is.
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
A♭add9/C
x041
A♭add9/E♭
8a8b
A♭add9/B♭
3043
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.