Place a drip pan or other container on the side of the mower with the filler. Carefully tilt the mower so oil drains out and into the pan. Discard the spent oil into a proper disposal vessel. Now slowly pour fresh oil into the mower. For the specific type of oil you need check your instruction manual. Make sure to add only as much as your particular model requires. Remember to let the mower sit undisturbed for a few minutes so the oil settles properly inside the engine.
Other items and supplies include a plastic drip tray motor oil and a container for waste oil. Often a large piece of cardboard is useful as well an old rag or cloth. Also know that this guide deals with push or self-propelled mowers not riding mowers. While some advice here applies they are another animal altogether.
Get out there and mow Now that you have done all that your mower should be ready to tackle the season in stride. It should run smoother and more safely too. Even better you have just saved the $200 to $300 fee it typically costs at least in my neck of the woods to have your lawn mower serviced professionally. So go on and get out there. That high grass needs cutting.