Speed control of a DC motor using variac
You can't directly.  A variac is a transformer, usually a autotransformer, but in either case puts out AC.

You could rectify the AC to make DC by using a full wave bridge if you truly have a DC motor.

More likely, what you have is not a DC motor.  This machine looks old, and considering it was intended to have variable speed, it could be a brushed motor that is commutated so as to work directly with AC.  Such motors do work with DC too, but always spin in one direction regardless of the polarity of the applied voltage.

This is just a guess, but the extra stuff on the bottom of the variac could be for automatically moving the wiper as part of a control system.