The standard grips this chord is usually shown with.
Eaug7 is E, G#, B# and D, a augmented seventh. The shape this page opens on is written 030110, lowest string first.
Note by note. E is the root, G# is the major third, B# is the sharp fifth and D is the flat seventh.

Also written E7#5, E+7 or E7(#5). The same chord either way; which spelling you meet depends on who wrote the chart.
There are 6 common shapes for Eaug7 on the guitar, and 30 derived voicings in 4 families.
One note away. Change a single note of Eaug7 and you have Emaj7#5 (with one note moved), E7 (with one note moved), E7b5 (with one note moved), Ealt (with one note added), Eaug (with one note taken away) or Eaug9 (with one note added).
The common shapes, written lowest string first: 030110, xx2534, x767x8, x-7-10-7-9-8, 12-11-12-x-13-x, 12-x-12-13-13-x.
Under the hand. 1 of the 6 shapes here sits in open position, and the first uses 3 open strings. None of them needs a barre. Together they cover the neck from the 1st fret to the 13th.
Where it goes. Eaug7 is a dominant with its tension raised, so it still points at A — 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. Eaug7 has 0565xx, 0x011x, x7x798, 12-x-12-13-13-x.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. Eaug7 has x3213x, xx0110, 0301xx, x5655x, 8767xx, x-x-10-9-9-10, 10-11-10-9-x-x, x-x-12-13-13-12.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. Eaug7 has x3x130, 0x011x, 4x253x, x5x554, 8x675x, x7x798, x-11-x-9-13-10, 10-x-10-9-9-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. Eaug7 has 4300xx.
Tensions. A shell of Eaug7, root, third and seventh, leaves a string free, and the tones that belong over it are the b9 (F), the 9 (F#), the #9 (F##) and the #11 (A#).
What kind of chord this is. Eaug7 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.