The C7(#9) belongs to the category of altered dominant 7th chords (general: V7alt). That are dominant 7th chords with one or more of the altered tensions b9, #9, b13 or #11, in which #11 has a special role. Please look up the description for the 7(#11) chord type. Altered tensions mainly occur, when the V7 chord resolves from V to I, like from the C7 to Fmaj7 or Fm7. Instead of specifying certain tensions like #9, altered chords are often notated in a very universal way: written as C7alt the player can decide by himself which tensions he/she wants to use (the versatile guitar player will always decide by himself anyway…).
theoretically the C7(#9) consists of the tones
C (1), E (3), G (5), Bb (7) und D# (#9). On the guitar you will in most cases omit the 5th or, if it is located on one of the higher strings, move it up to the b13 by one fret. That gives a C7(#9,b13), but as I mentioned before altered chords are very interchangeable anyway. If the 5th lays down low, directly above the root (which in this case also is the lowest note), you may want to keep it.
The #9 is located an augmented 2nd above a root tone, which equates a minor third. Since the names of two chord tones should (theoretically) never be deduced from one note, the note name of the #9 often has double accidentals: for example E7(#9) has the major 3rd G#, therefore the #9 cannot be G, it's F##! Practically, especially verbally, you'll probably take it easier.
As a tonic chord in blues, funk, etc. where the root of a dominant 7th chord defines the key (a „blues in F“ starts with an F7 on the first degree), the 7(#9) can be played over several bars without creating the feeling that it needs to resolve to a certain chord. The song „Purple Haze“ by Jimi Hendrix is an often mentioned example in that context. For that reason the 7(#9) chord, especially the E7(#9), is often called the „hendrix chord“.
In chord progressions where an altered chord resolves to a minor chord, 7(#9) may be prefered over 7(b9) or 7(b13). For example: Gm7(b5) C7(#9) Fm9
or Bbm7 C7(#9) Fm9
or Dbmaj7 C7(#9) Fm7
It's also very common to combine several alterations within one bar: Gm7(b5) C7(#9) C7(b9) Fm7 Bbm7 C7(#9) C7(b13) Fm9
The C7(#9) can also be written C7#9 without the brackets. The readability doesn't suffer from that here.