With the exception of big commercial mowers or larger garden tractors, just about every lawn mower is going to have a simple single-cylinder engine. That means they're pretty easy to service, including changing the spark plug.
Older mowers used a magneto to supply current for ignition, but newer designs often feature electronic ignition for spark. Either way, the method of changing the spark plug on the lawn mower should be the same.
This is a good project for new DIYers
With the mower on level ground, remove the engine cover or heat shield (if applicable).
Remove the spark plug wire from the plug and insulator.
Fit the spark plug socket over the plug and turn counterclockwise until the plug is removed.
Installation is the reverse of removal—just screw in the new plug and make sure it's torqued down snugly enough to not loosen up again, reconnect the plug wire, and reinstall the cover (if applicable).
Many new spark plugs for mowers will come pre-set with the appropriate electrode gap. It's still a good idea to check the gap with the proper feeler gauge so you can be sure that the plug is gapped properly.
NOTE: Often, the plug doesn't really need to be replaced. Still, pull the plug out and have a good look. If it doesn't appear burned, eroded, or fouled, set the gap again, clean it with a wire brush and some solvent (aerosol brake cleaner will work fine) and reinstall it.