The standard grips this chord is usually shown with.
Cmaj7 is C, E, G and B, a major seventh. The shape this page opens on is written x32000, lowest string first.

Also written CM7, CΔ7, CΔ, Cma7 or C major 7. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 8 common shapes for Cmaj7 on the guitar, and 32 derived voicings in 4 families.
In which keys. Every note of Cmaj7 belongs to C major (the I), E minor (the ♭VI), G major (the IV) and A minor (the ♭III).
The common shapes, written lowest string first: x32000, x3241x, x35453, xxx557, xx5557, 8-10-9-9-8-8, x-x-10-12-12-12, x-15-14-12-12-12.
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. Cmaj7 has x324xx, 879xxx, x3x45x, 8x99xx.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. Cmaj7 has x2201x, 3324xx, x3545x, xx5557, 7755xx, xx9988, 8-10-9-9-x-x, x-x-10-12-12-12.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. Cmaj7 has 3x241x, x2x010, x3x453, x7x587, 7x555x, x-10-x-9-12-8, 8x998x, 12-x-10-12-12-x.
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. Cmaj7 has 030453, 005557, 000002, 00050x, 03000x, 00400x.
Tensions. A shell of Cmaj7, root, third and seventh, leaves a string free, and the tones that belong over it are the 9 (D), the #11 (F#) and the 13 (A).
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.