The standard grips this chord is usually shown with.
Caug is C, E and G#, a augmented triad. The shape this page opens on is written x3211x, lowest string first.

Also written C+, C(#5) or C augmented. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 8 common shapes for Caug on the guitar, and 46 derived voicings in the triad family.
The common shapes, written lowest string first: x3211x, x3x554, x3655x, xxx554, 87655x, 8-x-10-9-9-8, x-x-10-9-9-8, x-x-14-13-13-12.
Triad. Three notes across one string set. Caug has x321xx, xx211x, xxx110, x3211x, 0321xx, xx2110, 432xxx, xxx554.
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.