With the AC motor with a single field winding (most common), you just reverse the two brush leads to reverse the motor direction.
With the AC Motor with a dual-field winding, you change which field winding is connected to one of the brushes.
In either case, the field coil is frame ground, the other lead of the field coil goes to one motor brush, and the hot side of the power goes to the other brush.
Yes, these are also called "Universal motors", and will run on DC the same as AC. To reverse direction, you still swap the brush leads, swapping the power to the whole brush/field wiring would not reverse the motor.
