The standard grips this chord is usually shown with.
D13 is D, F#, A, C, E and B, a dominant thirteenth. The shape this page opens on is written xx0412, lowest string first.

Also written Ddom13 or D dominant 13. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 9 common shapes for D13 on the guitar, and 53 derived voicings in 5 families.
In which keys. Every note of D13 belongs to E minor (the ♭VII) and G major (the V).
The common shapes, written lowest string first: xx0412, x54577, x54557, 555577, 10-7-9-7-7-8, 10-9-0-9-0-8, 10-9-9-9-10-8, 10-10-10-11-12-12, 10-12-10-11-12-10.
Shell. Root, third and seventh: the guide tones fix the quality, so the fifth is dropped. That is what leaves a string free, so pick a tension to put on top. D13 has xx0577, x5x577, 10-x-10-11-12-x.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. D13 has 2304xx, x3443x, xx9778, 8997xx, x-x-10-11-12-10, xx0412, xx4537, 7545xx.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. D13 has 2x041x, x3x432, 7x453x, x5x577, 8x977x, x-14-x-11-13-10, 10-x-10-11-12-x, x-9-x-7-12-8.
Rootless. The root left to the bass player. Frees a finger for a tension. D13 has x3445x, xx7577, xx9978, x-x-10-11-12-12, x-12-10-11-12-x, xx2412, x2421x, x2x212.
Open string. An open string left ringing against a fretted grip. Because it costs no finger, it sounds a note the closed shape has none left for -- a tension on top, or a pedal root underneath. Either a familiar grip with open strings added, or a shape so sparse the open strings carry the chord. These belong to their key rather than to a shape, so D, A, G and E have many and Eb a handful. D13 has 03443x, x34430, 030432, 0x7577, x04557, 754500.
Tensions. A shell of D13, root, third and seventh, leaves a string free, and the tones that belong over it are the #11 (G#).
The common shapes and the derived voicings come from different places, and both are explained in where the chords and the theory come from.
Shows each chord the way this style would voice it, and marks which of its alternatives belong to the idiom.