There is probably a diagram somewhere here but not complicated. IF there is only one small wire terminal on the solenoid, make very sure that mounting surfaces are bright as it is self grounding thru mount. IF there are two small terminals, one goes to ground. In both cases one small wire goes to ignition switch post that is hot when switch is in start position.
The cable from the battery is connected on one of the large posts and the other goes to starter, doesn't matter which.
NOW, there will likely be a small red wire junctioning on the large post where the battery cable attaches to the solenoid OR there may be two. One will go to the ignition switch to furnish power to it. The other will come directly from the alternator OR the alternator wire may go to the switch and back to the battery cable thru the wire mentioned first, depends on the mower.