Turn off your lawn mower and remove the keys from the ignition, then open the engine hood.
Find the oil dipstick on the base of the side of the engine. There is a plug on this base. Unscrew the plug.
Drain all the oil out into a pan and then screw the plug back into place.
Find the circular flywheel part on the engine assembly. Take the bolts out of the flywheel's cover with a socket wrench. Remove the cover.
Fit a flywheel holder over the lawn mower's flywheel. Have a friend hold the flywheel holder down as you take out the flywheel nut with your wrench. The flywheel nut is at the center of the flywheel.
Fix the flywheel holder's two arms onto the exterior of the sides of the flywheel. There is a bolt on the center of the flywheel holder. Tighten it with your wrench until the flywheel pops free from the engine assembly.
Find the oil pan on the bottom of the lawn mower's engine and remove its bolts. Pull the pan off once its bolts are removed. This reveals the PTO shaft.
Look along the long, distinctive PTO shaft for its two bolts. Remove both with your wrench.
Strike the top center of the engine assembly with a rubber mallet, just under where you removed the flywheel. This should cause the PTO shaft to come free. Strike more than once if necessary.
Pull out the old PTO shaft and slide the replacement shaft into place.
Follow your removal procedures in reverse to install the new PTO and secure it into place.