The standard grips this chord is usually shown with.
C#6 is C#, E#, G# and A#, a major sixth. The shape this page opens on is written x4332x, lowest string first.

Also written C#maj6, C#M6 or C# major 6. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 9 common shapes for C#6 on the guitar, and 26 derived voicings in 3 families.
In which keys. Every note of C#6 belongs to C# major (the I), Eb minor (the ♭VII), F minor (the ♭VI), F# major (the V), Ab major (the IV) and Bb minor (the ♭III).
The common shapes, written lowest string first: x4332x, x46666, x86666, 988666, 686696, 9-x-8-10-9-x, 9-x-11-10-11-9, 9-11-x-10-11-9, x-x-11-13-11-13.
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. C#6 has x433xx, 988xxx, x4x36x, 9-x-8-10-x-x.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. C#6 has x1312x, xx3324, 4433xx, xx6666, 6866xx, x-x-8-10-9-9, x-11-11-10-11-x, x-x-11-13-11-13.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. C#6 has x1x121, 4x332x, x4x364, x8x696, 6x666x, 9-x-8-10-9-x, x-11-x-10-11-9, 13-x-11-13-11-x.
Tensions. A shell of C#6, root, third and seventh, leaves a string free, and the tones that belong over it are the 9 (D#) and the #11 (F##).
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.