The standard grips this chord is usually shown with.
Fm7b5 is F, Ab, Cb and Eb, a half-diminished seventh. The shape this page opens on is written 1x110x, lowest string first.

Also written Fø, Fø7, Fm7-5, Fm7(b5) or F half diminished. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 9 common shapes for Fm7b5 on the guitar, and 28 derived voicings in 3 families.
In which keys. Every note of Fm7b5 belongs to Eb minor (the ii°) and F# major (the vii°).
The common shapes, written lowest string first: 1x110x, 123141, xx3444, x86867, x8989x, x-x-9-10-9-11, 13-11-13-13-0-x, 13-x-x-13-12-11, 13-x-13-13-12-x.
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. Fm7b5 has 1x110x, x8x897, 13-x-13-13-12-x, 1664xx, x-8-13-13-12-x.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. Fm7b5 has xx1101, 1211xx, xx3444, x6646x, 7868xx, xx6867, x8989x, x-x-9-10-9-11.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. Fm7b5 has x2x141, 1x110x, 4x344x, x6x464, 7x686x, x8x897, 11-x-9-10-9-x, x-11-x-10-12-11.
Tensions. A shell of Fm7b5, root, third and seventh, leaves a string free, and the tones that belong over it are the 11 (Bb) and the b13 (Db).
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.