The standard grips this chord is usually shown with.
Fmaj9 is F, A, C, E and G, a major ninth. The shape this page opens on is written 102010, lowest string first.

Also written FM9, FΔ9, Fma9 or F major 9. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 13 common shapes for Fmaj9 on the guitar, and 46 derived voicings in 5 families.
In which keys. Every note of Fmaj9 belongs to C major (the IV), D minor (the ♭III), F major (the I) and A minor (the ♭VI).
The common shapes, written lowest string first: 102010, 132213, xx2213, xx3253, 533553, x85555, x8798x, 88798x, x-10-10-10-10-12, x-x-10-12-10-12, 13-10-10-10-10-12, 13-12-14-12-13-12, 13-x-14-14-13-15.
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. Fmaj9 has 1020xx, x8798x, 13-12-14-12-x-x, xx3253.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. Fmaj9 has 1020xx, x0305x, x8798x, 13-12-14-12-x-x, xx3253, 5859xx, xx5965, x-10-14-10-10-x.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. Fmaj9 has x0x051, 3x325x, x8x985, 5x596x, x-10-x-10-10-12, 13-x-14-12-10-x, x7x263, 12-x-7-10-8-x.
Rootless. The root left to the bass player. Frees a finger for a tension. Fmaj9 has xx2213, x0201x, xx5555, xx7988, x-10-10-9-10-x, x-x-10-12-10-12, x-12-14-12-13-x, x-x-14-14-13-15.
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. Fmaj9 has 030253, 000503, 530000, 57000x, 0x0005, 3x0200.
Tensions. A shell of Fmaj9, root, third and seventh, leaves a string free, and the tones that belong over it are the #11 (B) and the 13 (D).
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.