The standard grips this chord is usually shown with.
Cadd9 is C, E, G and D, a add nine. The shape this page opens on is written x32030, lowest string first.

Also written C(add9), Cadd2 or C add nine. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 8 common shapes for Cadd9 on the guitar, and 31 derived voicings in 3 families.
In which keys. Every note of Cadd9 belongs to C major (the I), D minor (the ♭VII), E minor (the ♭VI), F major (the V), G major (the IV) and A minor (the ♭III).
The common shapes, written lowest string first: x32030, x30030, x32x33, 870080, 87x788, x-x-10-9-x-10, x-15-14-12-15-12, x-15-14-x-15-15.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. Cadd9 has xx0010, x3203x, 0300xx, x5555x, x-x-10-9-8-10, 10-10-10-9-x-x, x-x-12-12-13-12, xx2533.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. Cadd9 has 0x001x, 3x253x, x5x553, x3x030, 8x575x, x7x788, 10-x-10-9-8-x, x-10-x-9-13-10.
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. Cadd9 has 0300xx, xx0030, 05005x, xx2030, 070050, 0x003x.
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.