The standard grips this chord is usually shown with.
Fm7 is F, Ab, C and Eb, a minor seventh. The shape this page opens on is written 131111, lowest string first.
Note by note. F is the root, Ab is the minor third, C is the fifth and Eb is the flat seventh.

Also written Fmin7, F-7 or F minor 7. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 7 common shapes for Fm7 on the guitar, and 31 derived voicings in 4 families.
One note away. Change a single note of Fm7 and you have Fm (with one note taken away), Fm6 (with one note moved), Fm7b5 (with one note moved), Fm9 (with one note added), FmMaj7 (with one note moved) or Fmadd9 (with one note moved).
In which keys. Every note of Fm7 belongs to C minor (the iv), C# major (the iii), Eb major (the ii), F minor (the i), Ab major (the vi) and Bb minor (the v).
The common shapes, written lowest string first: 131111, xx3544, x8686x, x8689x, x-8-10-8-9-8, x-x-10-10-9-11, 13-15-13-13-13-13.
Under the hand. None of the shapes for Fm7 uses an open string, so every one of them is movable; the lowest sits at the 1st fret. 3 of the 7 need a barre. Together they cover the neck from the 1st fret to the 15th.
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. Fm7 has x868xx, 13-11-13-x-x-x, 1x11xx, x8x89x, 13-x-13-13-x-x, 166xxx, x-8-13-13-x-x.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. Fm7 has xx1111, 1311xx, xx3544, x6656x, 8868xx, xx6868, x-8-10-8-9-x, x-x-10-10-9-11.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. Fm7 has x3x141, 1x111x, 4x354x, x6x564, 8x686x, x8x898, 11-x-10-10-9-x, x-11-x-10-13-11.
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. Fm7 has 4600xx.
Tensions. A shell of Fm7, root, third and seventh, leaves a string free, and the tones that belong over it are the 9 (G), the 11 (Bb) and the 13 (D).
What kind of chord this is. Fm7 is a minor chord — root, minor third, fifth. minor 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.