The standard grips this chord is usually shown with.
Dm7b5 is D, F, Ab and C, a half-diminished seventh. The shape this page opens on is written xx0111, lowest string first.

Also written Dø, Dø7, Dm7-5, Dm7(b5) or D half diminished. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 9 common shapes for Dm7b5 on the guitar, and 31 derived voicings in 3 families.
In which keys. Every note of Dm7b5 belongs to C minor (the ii°) and Eb major (the vii°).
The common shapes, written lowest string first: xx0111, x53534, x5656x, xx6768, x-8-0-10-9-8, 10-x-x-10-9-8, 10-x-10-10-9-x, 10-11-12-10-13-10, x-x-12-13-13-13.
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. Dm7b5 has xx0564, x5x564, 10-x-10-10-9-x, x-5-10-10-9-x, 10-8-10-13-x-x, 10-15-15-13-x-x.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. Dm7b5 has x3313x, xx0111, 1301xx, 4535xx, xx3534, x5656x, xx6768, 8867xx.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. Dm7b5 has 1x011x, x3x131, 4x353x, x5x564, 8x676x, x8x798, 10-x-10-10-9-x, x-11-x-10-13-10.
Tensions. A shell of Dm7b5, root, third and seventh, leaves a string free, and the tones that belong over it are the 11 (G) and the b13 (Bb).
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.