The design of the figure eight drive is very easy to construct, though insidiously difficult to envision.  It is easiest to conceptually split the two sides of the drive train into two sides, the “O-side” on the rider’s right, and the “8-Side” on the rider’s left.  The two sides are connected by shared axles at the top and bottom of the system.
The third prototype drivetrain (Prototype C1) and tricycle.
The top of the O-side is a standard crank, and the bottom is a standard freewheel mounted normally on the bottom hub.  The top of the 8-side is a freewheel mounted on the top axle such that it ratchets when the axle is rotated in the forwards direction (when pedaling forwards), and catches when the axle is rotated in the backwards direction (when pedaling backwards).  The bottom of the 8-side has a freewheel that is mounted in the same direction as the other bottom freewheel.  The fact that both bottom freewheels are mounted to ratchet in the same direction allows the tricycle to freewheel in the forwards direction.
The chain on the O-side is mounted in the normal fashion.  The chain on the eight side is crossed over (it’s a Möbius chain) and is passed through a tube on its slack side in order to prevent the two chains from grinding against each other.  The crossed chain is what makes the wheel rotate forwards when you are pedaling backwards.
Though the tricycle can freewheel in the forwards direction, the two chains prevent tricycle from moving backwards.  For the most part, this is a convenience, as one can pause while climbing an incline without concern for rolling backwards down the hill.  There are times, however, when moving the tricycle is necessary.  In order to allow this, the fork mounting is shaped in such a way as to allow the steering column to rotate 180 degrees and allow one to freewheel and actively propel oneself in reverse.
The fork in the standard (forwards) position.
The fork in the reverse position.