The standard grips this chord is usually shown with.
A7#9 is A, C#, E, G and B#, a seven sharp nine. The shape this page opens on is written x32223, lowest string first.
Note by note. A is the root, C# is the major third, E is the fifth, G is the flat seventh and B# is the minor third.

Also written A7(#9), A7+9 or A7♯9. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 9 common shapes for A7#9 on the guitar, and 43 derived voicings in 5 families.
One note away. Change a single note of A7#9 and you have Am7 (with one note taken away), Am9 (with one note moved), A7 (with one note taken away), A9 (with one note moved), A7b9 (with one note moved) or A/G (with one note taken away).
The common shapes, written lowest string first: x32223, 5455xx, x45555, 575688, 575658, xx7688, x77688, x-0-10-9-8-9, x-12-11-12-13-x.
Under the hand. None of the shapes for A7#9 uses an open string, so every one of them is movable; the lowest sits at the 2nd fret. 4 of the 9 need a barre. Together they cover the neck from the 2nd fret to the 13th.
Where it goes. A7#9 is a dominant with its tension raised, so it still points at D — harder than a plain seventh does, because the altered tones sit a semitone from where they are going.
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. A7#9 has 5455xx, xx7688, x-12-11-12-13-x.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. A7#9 has 5455xx, xx7688, x-12-11-12-13-x, x3522x, xx5525, x4758x, 8-10-7-6-x-x, x-10-10-6-10-x.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. A7#9 has x3x223, 5x552x, x4x585, 8x768x, x-10-x-6-10-8, x-12-x-12-13-9, 9-x-10-12-10-x, 15-x-11-14-13-x.
Rootless. The root left to the bass player. Frees a finger for a tension. A7#9 has x3202x, x4555x, x-x-10-9-8-9, x-x-11-12-13-12, x3x020, xx2523, x4x553, xx5658.
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. A7#9 has x02523, 5x5520, 03522x, x35220, 005525.
Tensions. A shell of A7#9, root, third and seventh, leaves a string free, and the tones that belong over it are the #11 (D#), the b13 (F) and the 13 (F#).
What kind of chord this is. A7#9 is an altered chord — a dominant seventh with its fifth or ninth moved. altered dominant 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.