Every fingering that fits a hand
5405
easy · no 5
5203
easy · no 5
5205
easy · no 5
520x
easy · no 5
5435
moderate
What is true of it
Cadd9 is C, E, G and D — 1, 3, 5 and 9 counted from C.
On an instrument that cannot reach all 4, the 5 goes first, in that order.
The easiest of the 5 fingerings below is 5405: 3 fingers, held at the 4th 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 C, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
Cadd9/E
9caa
Cadd9/G
0203
Cadd9/D
x203
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.