How does one tune up a gas lawn mower? (push mower).?

If there's nothing wrong with it and you're just trying to keep it that way, then I suggest the following:

1. drain the oil and refill with fresh oil - use the weight suggested in the owner's manual. If you don't have the manual and can't find a copy online, then just use 5W-30 or 10W-30. Synthetic is best but not required.

2. Remove the air filter. If its really dirty then install a replacement. If it's not too bad, then just clean off as much dust as possible with an old paintbrush or compressed air and reinstall it.

3. Remove and check the spark plug. if the tip is fouled up or burnt, then install a new one, if not then you can reinstall it or replace it - your choice. Spark plugs are only a few dollars so I usually just replace it for good measure if its more than a few years old.

4. If its been sitting for a long time, consider draining the gas and putting in fresh gas. Modern gas contains 10% ethanol, it burns fine in gas engines but ethanol absorbs water when it sits for more than a few months. The best option is to buy ethanol free gas for your small gas engines. The second best option is to use the gas fast enough that its never sitting around (in cans or in the equipment) for more than 1-2 months. If you can't get ethanol-free gas and you want/need to store it longer, then add a fuel stabilizer additive in any gas you keep for use in small engines.