The standard grips this chord is usually shown with.
Ab7 is Ab, C, Eb and Gb, a dominant seventh. The shape this page opens on is written xx1112, lowest string first.

Also written Abdom7 or Ab dominant 7. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 6 common shapes for Ab7 on the guitar, and 32 derived voicings in 4 families.
In which keys. Every note of Ab7 belongs to C# major (the V) and Bb minor (the ♭VII).
The common shapes, written lowest string first: xx1112, 431112, 464544, xx6878, x-11-10-11-9-x, x-11-13-11-13-11.
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. Ab7 has 434xxx, x-11-10-11-x-x, 4x45xx, x-11-x-11-13-x.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. Ab7 has xx1112, 2311xx, xx4544, 4645xx, x6657x, xx6878, x-9-10-8-9-x, x-x-10-11-9-11.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. Ab7 has x3x142, 2x111x, x6x574, 4x454x, 8x687x, x9x898, 11-x-10-11-9-x, x-11-x-11-13-11.
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. Ab7 has 4x4500, 46450x, 4x4540, 2005xx, 2x050x.
Tensions. A shell of Ab7, root, third and seventh, leaves a string free, and the tones that belong over it are the b9 (Bbb), the 9 (Bb), the #9 (B), the #11 (D), the b13 (Fb) and the 13 (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.