To clean it first start with a cool engine. If your mower has a fuel valve switch it off. If you can disconnect the spark plug too. Next use a leaf blower to blast away any old dirt and major debris. Now gently lay the mower on its side fuel cap facing up. Try to get rid of any junk on the mowers underside as well.
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.
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.