Most modern lawn tractor mowers have sophisticated engines with pressure lubrication and oil pumps, just like automotive engines. Oil pumps make possible full-flow filtering, meaning that all oil circulated by the oil pump first passes through an oil filter to remove harmful particulates. Most particulates are highly abrasive carbon which results from combustion and high temperatures. It is therefore imperative to change oil and oil filters regularly.
Locate the engine oil drain and fill plugs. Warm up the tractor's engine, and turn the tractor so the oil drain plug faces slightly downhill if possible. Turn off the engine. Position the drain over a container large enough to accept all the drain oil.
Unscrew the oil plug, making sure the oil runs into the container. Use a funnel if necessary. Open the fill plug or cover to allow air into the crankcase, increasing the oil's flow rate. Use vinyl gloves to isolate your hands from the very warm oil, and do not drop the plug into the container.
Replace the oil drain plug when the oil stops dripping steadily.
Re-locate another container under the oil filter. Loosen the filter by hand if possible. If not, use a filter wrench. Unscrew the filter, and lower into the container. Wipe the filter mounting pad on the engine with an absolutely clean paper towel or rag.
Pour a bit of new oil into the filter to wet the filtrate which will speed re-pressurization. Put a thin coating of clean oil on the new filter's gasket, and gently thread onto its mounting pad. Make sure it spins freely so it doesn't cross thread. Tighten to ¾ turn past the first contact point or per manufacturer's instructions.
Check the drain plug and filter for tightness. Fill the engine with the prescribed amount of new oil of the correct grade and weight. Check the level, and replace the fill cover or plug.
Start the engine and let it run, making sure that there are absolutely no leaks from the filter's gasket. Stop the engine, and check the oil level again.
Pour the drained oil into a proper recycling container from the drain containers and the old filter. Follow instructions for your locale relevant to proper filter and oil disposal or recycling.