The way you change the oil on a lawn mower will depend on whether the lawn mower is a riding lawn mower or a push lawn mower.
If it's a riding lawn mower there should be a plug near the oil dip stick where you check the oil.
It could either be a plug that takes a wrench or could be a plug that requires a ratchet that you just place into the oil plug to remove it.
You then just remove the oil drain plug on the riding lawn mower engine and use a oil pan to catch the old oil and then if the lawn mower has an oil filter you remove the oil filter with an oil filter wrench and then wipe the old oil off the oil filter mount and then apply fresh oil to the rubber seal of the new oil filter and then hand tighten the new oil filter on if it has one.
If it doesn't have an oil filter then just skip the step of the oil filter and once the oil is drained just put the plug back in and add fresh oil until it's full.
Be careful to not overfill your lawn mowers engine with too much oil because it can result in damage to the engine.
Add a little oil at a time and keep checking it until it's full.
If it's a push lawn mower the oil drain plug will be underneath the mower so you'll have to put the push mower up onto a table or something else such as two sawhorses with a couple 2 x 4 lumber holding it up to allow an oil drain pan to sit underneath to catch the oil.
Then use a tool that fits into the oil drain plug to remove the oil drain plug.
Sometimes it's just a regular ratchet and sometimes it may be another hex tool or large Allen Wrench to remove it.
Then let the oil drain out once the plug is removed and once the oil is drained replace the plug and refill with oil a little at a time until it's filled back up with oil.