As for the Aspen, I have mine hooked up to an STEC AP. It should work the same. To fly with the GPSS connected to the AP, the autopilot needs to be in HDG (or whatever gives you a heading control on the Century) and ALT if you have altitude hold. In this mode, you can fly the plane using the heading bug on the Aspen (right knob and it defaults as the thing that changes if you start turning it).
To fly using GPSS, you need to have the center button on the Aspen set to a valid GPS signal (GPS 1 or GPS 2) and have a flight plan in the GPS. Then select the GPSS button on the right side of the Aspen. It will be green when it is active. It will be yellow if something is wrong. And it will be gray if it is not active.mthen watch the magic happen...
If you are flying a conventional NAV signal (VOR or ILS), you would select it on the Aspen and use the NAV button on the autopilot. If the approach has a GPS overlay, you can have the GPSS fly it up to the FAF and then switch over to VLOC or VOR1 or the ILS signal before reaching it. You would then go into APR mode.
The important thing is to understand how your hardware works together while you are on the ground -- much easier that way.
Here is an example of an LPV approach using my Aspen with a GTN and the AP.
http://youtu.be/o-B_9SzekTo