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.
Note by note. D is the root, F is the minor third, Ab is the flat fifth and C is the flat seventh.

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.
One note away. Change a single note of Dm7b5 and you have Ddim (with one note taken away), Ddim7 (with one note moved), Dm7 (with one note moved), DmMaj7b5 (with one note moved) or D7b5 (with one note moved).
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.
Under the hand. 1 of the 9 shapes here sits in open position, and the first uses 1 open string with 2 left unplayed. 4 of the 9 need a barre. Together they cover the neck from the 1st fret to the 13th.
Where it goes. Dm7b5 is the ii of C minor, which is where it is nearly always found: half-diminished, then an altered dominant, then the minor tonic.
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).
What kind of chord this is. Dm7b5 is a diminished chord — root, minor third, flat fifth. diminished and half-diminished chords on every root, and what they are for.
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.