Open up the engine hood of your lawn tractor and examine the spark plug. There should be a slender black wire that connects to the spark plug. This plug wire will cause the plug to fail if it is disconnected. Reinsert it if necessary.
Check the battery and ensure both the positive red wire and negative black wire are still connected to the separate sides of the battery via its bolts. Replace the wire(s) over the bolt(s) as necessary, and tighten them in place by twisting the bolts clockwise using a socket wrench.
Disconnect the red positive wire from the battery before troubleshooting further if the lawn tractor still won't start. This is for your safety.
Find the lawn tractor's solenoid by following the red positive wire as it leaves the battery and runs back to a part located between the battery and the tractor's engine. This part is the solenoid, and the red wire should connect to a bolt on its side. If it does not, reconnect it by utilizing the socket wrench to tighten it over the bolt just as you did with the battery.
Reconnect the red positive wire to the battery after you finish with the solenoid.
Replace the spark plug if the lawn tractor still will not run. Disconnect the plug wire from the spark plug, pull the plug out, and then connect the plug wire to the new plug.