Every fingering that fits a hand
0502
easy · no 5, 9
0412
easy · no 5, 9
What is true of it
G13 is G, B, D, F, A and E — 1, 3, 5, b7, 9 and 13 counted from G.
On an instrument that cannot reach all 6, the 5, 9 and 1 go first, in that order.
The easiest of the 2 fingerings below is 0502: 2 fingers, 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.
It leaves out the 5 and 9. 4 strings cannot carry 6 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 G, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
G13/B
4500
G13/D
7577
G13/F
x502
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.