Every fingering that fits a hand
6704
easy
6434
hard
643x
easy
6797
hard
What is true of it
C♯dim is C♯, E and G — 1, b3 and b5 counted from C♯.
The easiest of the 4 fingerings below is 6704: 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.
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
C♯dim/E
x434
C♯dim/G
010x
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.