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.
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.
For the past three years we have used the Greenworks 22502 Corded Lawn Mower on our ¼-acre lawn. We particularly like how easy it is to adjust the blade height and it is surprisingly light. There are just a couple negatives we have noticed. We live in the Pacific Northwest where mowing wet grass is unavoidable. When the grass is wet it does not feed into the bag of this mower easily. Also we had to replace the cord after my teenager ran over it with the mower. So cord control is important and takes a little planning.