A Minor Family Chords

The A minor family of chords consists of chords that are related to the A minor scale. 

From the notes of the A minor scale, you can build a triad (three-note chord) on each scale degree. These are:
Triads in A minor :

A minor (Am): A - C - E (root chord)
B diminished (Bdim): B - D - F
C major (C): C - E - G
D minor (Dm): D - F - A
E minor (Em): E - G - B
F major (F): F - A - C
G major (G): G - B - D


Adding a 7th to each triad creates more complex chords:
Seventh Chords in A Minor:

Am7: A - C - E - G
Bm7♭5 (half-diminished): B - D - F - A
Cmaj7: C - E - G - B
Dm7: D - F - A - C
Em7: E - G - B - D
Fmaj7: F - A - C - E
G7: G - B - D - F.

Here are a few examples of progressions using chords in the A minor family:
Typical Progressions in A Minor:

Am - Dm - E - Am (natural minor)
Am - F - G - Am (natural minor)
Am - G - F - E (harmonic minor for E major or E7)
How They Work Together
Am (tonic): The "home" chord of the key.
E or E7 (dominant): Provides tension and resolution back to Am.
F and G: Borrowed from natural minor, giving a sense of movement.
Dm (subdominant): A smooth transition chord.