Am/C is C, A and E. The shape this page opens on is written x32210, lowest string first.
Note by note. C is the root, A is the sixth and E is the major third.

Also written Am over C or Am with C in the bass. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 6 common shapes for Am/C on the guitar.
One note away. Change a single note of Am/C and you have A (with one note moved), Adim (with one note moved), Asus2 (with one note moved), Asus4 (with one note moved), Am6 (with one note added) or Am7 (with one note added).
In which keys. Every note of Am/C belongs to C major (the vi), D minor (the v), E minor (the iv), F major (the iii), G major (the ii) and A minor (the i).
The common shapes, written lowest string first: x32210, x32555, x32255, x77555, x77558, 12-12-14-14-13-12.
Under the hand. 1 of the 6 shapes here sits in open position, and the first uses 1 open string with 1 left unplayed. 3 of the 6 need a barre. Together they cover the neck from the 1st fret to the 14th.
What kind of chord this is. Am/C is a slash chord — a triad over a named bass note. slash 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.