Real simple, but bear with me as the description is a little involved.
Under the middle of the train (between cars #4 and #5, I think) there is an entirely conventional chain clutch. Just as you would find under almost any coaster train.
On the lift there is a second track which runs between the main rails. This track starts below and behind the station, goes all the way to the top of the lift hill, and partway down the other side.
In this track is a catchwagon, which is a small, segmented train just over half the length of the trains we ride in. At the back of this catchwagon is a sleeved pin designed to engage with the chain clutch on the train. For all intents and purposes, it is a single chain link.
A large wire rope is attached to the front of the catchwagon. This rope runs all the way up and over the top of the lift hill, then down to the cable winding drum beneath the lift hill. This rope is the reason that the catchwagon is so long. The catchwagon attaches to the middle of the train, and there is a concave bend at the base of the lift, so the hoisting rope would rub against the bottom of the front of the train. The long catchwagon insures that the attachment point for the hoisting cable is a few feet ahead of the front of the train.
In the station, the catchwagon engages with the chain clutch on the train. The winding drum turns, pulling the cable over the crest of the hill, and taking the train with it. This is why the catchwagon track extends to the downhill side of the lift: it has to go far enough for the back end of the catchwagon to get past the uphill side of the lift hill, so that the train's center of gravity can get past the top of the hill. At that point, gravity takes over and rolls the train right off of the catchwagon.
This results in a problem. Now there is a big long catchwagon on the downhill side of the lift hill, its entire length extending beyond the hill peak. This is a precarious position as gravity will tend to drag it on down the downhill side of the lift, and unspooling the hoisting cable won't make it go back down the lift side. So, a second, smaller cable is attached to the back end of the catchwagon. That cable runs from the catchwagon, down the lift, to an idler under the back end of the station, then under the station to the same winding drum that the hoisting cable is attached to. This arrangement is such that as the hoisting cable is pulled in, the return cable is played out. Once the train disengages at the top of the lift, the winding drum is reversed and the return cable pulls the catchwagon back over the top of the hill so that it can roll back down into the station for the next train.
I hope that makes sense. If it doesn't, please ask questions!
--Dave Althoff, Jr.