Poulin lawn tractor makes a clicking noise but will not turn over.

The clicking noise is the solenoid (high power relay that connects and disconnects the starter motor). If the unit has headlights, turn them on and see if they are bright when trying to start the engine. If they go dim, either the battery is low or you may have bad connections, maybe even only at the solenoid. If the headlights remain bright when starting, chances are, you may have a bad solenoid or even a bad starter, or the (heavy) wiring from the solenoid to the starter, or maybe even a bad (rusty?) ground connection from the battery. Have you tried jumping the battery? Make SURE you are using the right voltage first!

I agree but would start by trying to jump it from my car or another battery. Dead or low battery is most common but everything infoguy said is possible