Next you will change the oil. To lower oil viscosity and get it moving freely run the engine for a few minutes. Now shut the engine off and roll the mower onto a piece of cardboard or drop cloth. Close the fuel line (if your mower has one) and unhook the spark plug as before. Find the oil filler tube and remove its cap. Often the cap also functions as a dipstick.
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.
I know that many people prefer to hose their mowers down with a garden hose. I admit I have done it. Still doing that is risky. If water gets into the wiring air filter or engine you could really do some damage. Hand washing with damp rag is a drag but also your safest bet.