Just for a summary point of view and my take, what Kirk and Fretsource and Alrightmax have said is:
The key of C has no sharps or flats (the 'base' key in understanding all the rest)
The key of A minor is a 'natural' minor scale. What that is saying is that the key of A minor is the relative minor key to the key of C major. Also, note that any relative minor of any major key will always be this Aeolian mode of the 'key of the moment' (the sixth position of the major scale while playing the same intervals as the major scale, only beginning in the sixth position).
Here's a lesson I recently finished on the topic,
An Intro to Modes