The standard grips this chord is usually shown with.
C#mMaj7b5 is C#, E, G and B#, a minor major seven flat five. The shape this page opens on is written x42010, lowest string first.
Note by note. C# is the root, E is the minor third, G is the flat fifth and B# is the major seventh.

Also written C#mM7b5 or C#m(maj7)b5. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 6 common shapes for C#mMaj7b5 on the guitar, and 28 derived voicings in 4 families.
One note away. Change a single note of C#mMaj7b5 and you have C#dim (with one note taken away), C#dim7 (with one note moved), C#maj7b5 (with one note moved), C#m7b5 (with one note moved) or C#mMaj7 (with one note moved).
The common shapes, written lowest string first: x42010, x4x553, x4555x, 9-10-x-9-8-8, 9-10-10-9-x-9, x-x-11-12-13-12.
Under the hand. 1 of the 6 shapes here sits in open position, and the first uses 2 open strings with 1 left unplayed. 2 of the 6 need a barre. Together they cover the neck from the 1st fret to the 13th.
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#mMaj7b5 has x4x553, 9-x-10-9-8-x, 9-7-10-12-x-x.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. C#mMaj7b5 has x3202x, x4555x, x-x-10-9-8-9, 9-10-10-9-x-x, x-x-11-12-13-12, 3425xx, xx2523, xx5658.
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#mMaj7b5 has 3x252x, x3x020, x4x553, 8x565x, x7x688, 9-x-10-9-8-x, x-10-x-9-13-9, 12-x-11-12-13-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. C#mMaj7b5 has 002523, 0055xx, 0340xx.
Tensions. A shell of C#mMaj7b5, root, third and seventh, leaves a string free, and the tones that belong over it are the 11 (F#) and the b13 (A).
What kind of chord this is. C#mMaj7b5 is a diminished chord — root, minor third, flat fifth. diminished and half-diminished chords on every root, and what they are for.
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.