The standard grips this chord is usually shown with.
A7 is A, C#, E and G, a dominant seventh. The shape this page opens on is written x02020, lowest string first.

Also written Adom7 or A dominant 7. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 9 common shapes for A7 on the guitar, and 36 derived voicings in 4 families.
In which keys. Every note of A7 belongs to D major (the V) and B minor (the ♭VII).
The common shapes, written lowest string first: x02020, x02223, xx2223, 542223, 575655, x07989, xx7989, x-12-11-12-10-x, x-12-14-12-14-12.
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 has 545xxx, x056xx, x-12-11-12-x-x, x0x02x, 5x56xx, x-12-x-12-14-x.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. A7 has xx2223, 3422xx, x0202x, xx5655, 5756xx, x7768x, xx7989, x-10-11-9-10-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 has x4x253, 3x222x, x0x020, x7x685, 5x565x, 9x798x, x-10-x-9-10-9, 12-x-11-12-10-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. A7 has 545000, 57560x, 5x5600, 34220x, x05600, 04400x.
Tensions. A shell of A7, root, third and seventh, leaves a string free, and the tones that belong over it are the b9 (Bb), the 9 (B), the #9 (B#), the #11 (D#), the b13 (F) 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.