Minor scales are just like major scales, but with different intervals. The minor intervals go like this:
Tone, Semitone, Tone, Tone, Semitone, Tone, Tone.
Notice that if you start on the third note of a minor scale, you have the same intervals as a major scale! Magic ain't it?
To figure out how many sharps or flats are in a minor key signature, you need to figure out the relative major key. The relative major is always three semi-tones above the minor. I remember this because a minor soldier in an army has to move UP to become a major. I don't know if they have a position called 'minor' in the army though. Anyway.
So, if you're playing in the key of A minor, if you move three steps up, you get to C (A to A#, A# to B, and B to C). Thus, C major is the relative major of A minor. So A minor has the same number of sharps or flats as C major –– except that in this case C major has no sharps or flats, so neither does A minor.