I need help in hooking up a solenoid on a '95 Honda 300 4 trax ATV. There are 4 wires that need hooking up. Thanks.

A solenoid, is like a relay. If this is Starter, then you will have 2 large terminals, one goes to battery positive, the other to starter. You now need 2 more wires to energize the solenoid. You need a hot and a ground, one side could always be grounded, and when you turn key, Or Push button it will provide the hot.
For safety, you could have the ground for the solenoid, hooked to Neutral switch. Then it could only be started in Neutral. Or maybe better is Handlebar Clutch switch, that way you can start in gear, provided clutch is pulled in.

"A solenoid, is like a relay" I like to describe the solenoid as a remote control switch. When you turn the key and energize the solenoid it closes its internal switch to power the starter.