Its technically a railroad hand cart...
Its nick-name is a GANDY DANCER!
Its and interesting but rather simple matter of mechanics.
As this diagam shows:
http://prr.railfan.net/diagrams/prrdiagr...
The handles rotate the gear connected to the driving axle. The connection of the handles to the gear works EXACTLY like the crankshaft on a internal combustion cylinder engine. One side pushes the connection to the gear down as the other moves up and then vice-versa.
Direction is determined simply by pushing the cart and getting it started in the direction its going. From there its just a matter of pumping.
I have had the chance on multiple occasions to operate one of these at a local museum, and its a load of fun...
We didn't have much track laid at the time but we got going over 25 miles per hour.. On a long stretch of level or downhill track, its not out of the question to get going near 50mph plus.
The only problem is braking. Simply a piece of leather or rubber on a block thats depressed by the foot against a wheel.