We will start by transforming the iv degree chord of the A minor key into an augmented sixth chord.
Below is the i - iv - V - i progression in A minor:
now, we set the iv degree chord in first inversion:
by raising the root of the iv degree chord a half-step (D# in this case) we get an augmented sixth chord:
The chord receives the name of Augmented Sixth chord because of the augmented sixth interval between the bass and the chromatically raised note. By raising this note we increase the harmonic tension. The augmented sixth interval resolves by moving the higher note up (D# - E) and the lower note down (F - E) by half steps. Listen to both examples:
Very often the Augmented Sixth chord is followed by the tonic chord in 2nd inversion before resolving to the dominant chord: