The standard grips this chord is usually shown with.
Cm7b5 is C, Eb, Gb and Bb, a half-diminished seventh. The shape this page opens on is written x31312, lowest string first.

Also written Cø, Cø7, Cm7-5, Cm7(b5) or C half diminished. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 7 common shapes for Cm7b5 on the guitar, and 28 derived voicings in 3 families.
In which keys. Every note of Cm7b5 belongs to C# major (the vii°) and Bb minor (the ii°).
The common shapes, written lowest string first: x31312, x3434x, xx4546, 8xx876, 8x887x, 8-9-10-8-11-8, x-x-10-11-11-11.
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. Cm7b5 has x3x342, 8x887x, x3887x, 8-6-8-11-x-x, 8-13-13-11-x-x.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. Cm7b5 has 2313xx, xx1312, x3434x, xx4546, 6645xx, xx8878, 8988xx, x-x-10-11-11-11.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. Cm7b5 has 2x131x, x3x342, 6x454x, x6x576, 8x887x, x-9-x-8-11-8, 11-x-10-11-11-x, x-13-x-11-13-11.
Tensions. A shell of Cm7b5, root, third and seventh, leaves a string free, and the tones that belong over it are the 11 (F) and the b13 (Ab).
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.