1. The root is a flatted 6th scale degree.
2. An augmented sixth is then added above the root.  Hence the name.

The next step is the filling of whats in between these two notes.  There are four different ways to do so.

Italian Augmented Sixth Chord (It+6) - only one to just three notes - third note added is a major third above the root

French Augmented Sixth Chord (Fr+6) - add a major third above the root - add an augmented fourth above the root

German Augmented Sixth Chord (Gr+6) - add a major third above the root - add a perfect fifth above the root - sounds like a dominant seven chord built on the flatted 6th scale degree 

Double-Augmented Sixth Chord (DA+6) - add a major third above the root - add a double augmented fourth above the root