Every fingering that fits a hand
5330
easy
5350
easy · no 5
5353
hard · no 5
5756
moderate · barre
535x
easy · no 5
What is true of it
Cm6 is C, E♭, G and A — 1, b3, 5 and 6 counted from C.
These are also the notes of Am7♭5/C. Which name is right depends on what is underneath and what came before — the notes alone do not decide.
On an instrument that cannot reach all 4, the 5 goes first, in that order.
The easiest of the 5 fingerings below is 5330: 3 fingers, held at the 3rd 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.
1 of the 5 need a barre.
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
Cm6/E♭
x353
Cm6/G
0353
Cm6/A
2333
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.