After sharpening both sides of the blade place it on the kits cone-shaped balancer. If one side dips below the other continue sharpening it until the blade rests level. Return the sharpened blades to the mower and reattach. If you have a torque wrench its a good idea to use it here. Often you need to tighten the blade mounting bolt/bolts to a specific tightness level. Typically measured in pound-feet your instruction manual should list these specs. For example my personal machine the Honda HRR216VKA between 36 to 43 lb-ft of torque is required.
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.
Gather what you need First gather your tools and equipment. You will need a power drill eye protection work gloves and a blade sharpening kit. The kit should come with a ceramic blade sharpener and balancer. Expect to pay about $8 for the kit at your local hardware store. You will also need a torque wrench (or a socket wrench in a pinch) and a wooden block. Consider having a rubber mallet on hand too.