The two halves should snap together with a bit of pressure. Be sure to have the clutch disengaged and carefully feed the belt onto the inside rim. The lip on the outer case will have to 'snap' over the roller edges. Depending on how often this has been done, you may need to support the drive unit somehow if the snap fit is not as tight as original. These units will not stand up well to frequent removal and reinstallation.
There should be a cable hanging somewhere to connect the drive unit motor, and ordinarily the autopilot has a switch on your panel somewhere or is switched with all your other instruments. If it's wired up hot then pressing the power button on the head should bring it up.
Sounds like you've got a bit of a treasure hunt on your hands as far as tracing wires etc to figure out what's been done (or undone!