I'm a beginning piano player and I have a piece of sheet music that describes a chord as Am (I'm assuming A minor). I don't understand how this chord is A minor when the notes are A-E-A. This chord is in the treble clef.
The given chord will be the underlying harmony. That does not mean that the notes at that point of time played by the piano will feature every note in A minor, nor does it mean that nothing but notes fitting an A minor chord will be present.
It just means that if another accompanying instrument were to play an A minor chord, this would fit with the music.
If you play yourself an additional C in some inconspicuous octave, the result should still sound in-key as compared to yourself playing a C# (which would fit into A major in contrast).
If the notes are
A-E-A, the chord is indeed ambiguous. It could be an A or Am chord.
However, the context can often tell you what the chord is supposed to be, even if the third (C# in case of A chord, C in case of Am chord) is missing. For instance, this chord will most likely be an Am chord if it appears in a C or Am key.
If the sheet music describes this chord as an Am chord, this is probably because they want to provide some more context to it. In case you'd like to improvise some adaptations to the piece, you'll now know that the chord is meant to be a minor chord, and should be used as such.
If it's on sheet music, it probably won't be describing the chord shown. More likely it will be telling you what chord can be played along with that bar/part bar of the music. There may be another part, for example, with just a G note for the bar, and the chord shown may be C. There will generally be chords shown, often for a chordal instrument like guitar to strum along with the piece. The only time that doesn't happen is when 'N.C.' is shown - 'no chord'.
You're right to assume it's minor. That's the 'm' bit.