Actually, finding and Am in the key of C is not that unusual. The chords you have available in the key of C are C, F, and G or G7, and Am, Dm, and Em (sometimes E or E7, depending). The chords are derived from building triads on the C scale, as follows:—

C, Dm, Em, F, G, Am, Bdim, and C again. Am is the relative minor of C, C is the relative major of Am. Both keys share the same notes, and in a sense, they could almost be regarded as one key. For songs in C, you can often use the relative minor chords to add color, and the same holds for songs in Am. But use them wisely. Too many chords can overpower a song.

This works for all other keys as well. The sequence, going up the major scale, is always:— major, minor, minor, major, major (often with added 7th), minor, diminished, and back to major. For most purposes, you can ignore the diminished chord. The G7 actually contains the Bdim triad inside it.

Modes are kind of a special case, and I won't complicate things by getting into them here.

Don Firth