I need to know the wiring system for a john deere riding mower on the solenoid

Hi,
Would be nice to know which model I am having to refer (LT 155s have three versions themselves with 2, 3 and 4 relays) but most Deere solenoids are 4 post affairs. They have two large posts for the large wires that connect to the battery and the starter. It does not matter which you hook to which BUT it is very important that the smaller wire with the large circular connector be also attached to the battery side (or your wiring harness has no power and nothing works!)
The two smaller posts are ground and trigger. They are often interchangeable also. The ground can, and sometimes is, merely "jumpered" to one of the mount bolts of the solenoid eliminating that.
In troubleshooting, make sure you actually did connect the harness connector to the battery side, believe me when I say that I have "pissed off" more than a few mechanics/technicians by bursting out in laughter at this common mistake. Beyond that I have seen people eliminate the ground by straight jumpers to ground (it is used in some safety systems - you can always apply/deny power or ground to the same effect.)
Peace,
Clarke