Use a socket wrench to remove the spark plug from the engine. Remove the plastic or metal engine cover on the lawnmower by loosening the cover bolts with a screwdriver or socket wrench, as needed. Use the socket wrench to remove the cylinder barrel and cap off the piston. Disconnect the remainder of the engine body from the lawnmower frame as well with the socket wrench.
Take apart each component of the lawnmower engine with crescent wrenches and the socket wrench. Use a photo camera to record each step of part removal. Put all the parts carefully in a 5-gallon bucket so that you don't lose any of the parts. Pour a 3-gallon container worth of kerosene or similar solvent in the bucket with the parts. Make sure to do this outside or a well-ventilated area with no flame source nearby.
Pull the engine parts out of the bucket one at a time and scrub them thoroughly with a plastic brush. Rinse off the kerosene and then place it on a flattened, large cardboard box for drying.
With crescent wrenches and the socket wrench, begin to reassemble the engine parts again as you took them apart. Refer to your photos to remember which part goes where. Use the engine circlips and a circlip tool to secure gears that may have been removed. Smear new engine oil on the inside of the cylinder before installing it. With the lower engine completed and the piston sticking out with the crankshaft arm, carefully slide the cylinder back onto the cylinder studs of the engine. Tighten down the cylinder and cap with the socket wrench and new washers and nuts.
Attach a new air filter and oil filter, and throw away the old ones. Insert a new spark plug into the cylinder and tighten it down carefully with the socket wrench. Reconnect the fuel line and engine oil line.
Start up the lawnmower by priming the carburetor and pulling the starter cord. Give the lawnmower about 30 seconds to warm up after ignition. Pull the throttle on the lawnmower so it rises to full speed. Run it for three to four minutes at this speed. Turn the mower off and let it cool down. Pour out the old engine oil to get rid of the engine deposits in the oil. Install fresh oil to complete the rebuild and replace the oil cap.