For example, my Dixie Chopper has a 25 HP Kohler, driving two pumps, and has hyd wheel motors. Each pump is a variable speed pump in that as you push or pull the lever for the pump, the machine will move forward or backward. You need two pumps because each one provides the fluid to run the hyd motors, one on each rear wheel at a certain speed. In a turn, you push one lever further than the other and you will turn in the direction of the slowest wheel motor. With the variable speed, you can creep along or race at full speed, which is usually about 6 to 10 MPH.
You say you don't know squat about hydraulics, but you need to understand the operation and limitations of a hyd system. I would be in the dark also if I just picked up several pieces of hyd hardware, and tried to jumble up something. You might just ruin the pumps and motors by now knowing. Hydraulics things have to match up to some degree. You learn by doing, reading, and more doing.
On one of my smaller Choppers, there is a belt from the engine that is turning two pumps, and the fluid not used is sent back to reservoir. As soon as I push on a lever, the pumps start pushing fluid to the wheel motors, and if you do this equal to both levers, you will travel in a straight line. If you slow one side, the machine will turn in that direction.
The reason they refer to them as zero turn, is that if you push one lever forward, and pull the other lever backward, you will turn the machine on a dime, so to speak.