Every fingering that fits a hand
x223
moderate · barre · no 5
7989
hard
768x
easy · no 5
7685
hard · no 5
7689
hard · no 5
What is true of it
D7 is D, F♯, A and C — 1, 3, 5 and b7 counted from D.
On an instrument that cannot reach all 4, the 5 goes first, in that order.
The easiest of the 5 fingerings below is x223: 2 fingers, one of them barring the 2nd fret, held at the 2nd 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.
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.
1 string stays silent.
Where its notes are on the neck
The brass dots are D, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
D7/F♯
bcac
D7/A
2223
D7/C
5220
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.