Assuming that you have checked the spark plug and confirmed that it has not completely failed, the most common reason is the magneto on that side has failed. (There is a separate magneto for each cylinder).
To replace a magneto, you'll need to look up which part is used on your particular engine. (You will need the brand (Briggs, etc.) and the complete engine model and type numbers from the id tag on the engine).
Then go to an intrernet parts seller and look up your part number. One place you can start at is at PartsTree
Once there, click on the engine icon for your engine and drill down until you find the correct magneto part number.
Replacing the magneto is simple, removing the top engine sheet metal cover involves removing a few bolts, and both magnetos are then readily available.
When installing the new magneto, you first screw it down at the furthest point away from the flywheel. Then rotate the flywheel so that the magnet is aligned with the new magneto.
As part of the new magneto, you will get a thin sheet of cardboard that you hold against the flywheel magnet and loosen the new magneto, allowing it to be pulled again the magnet (with the special cardboard spacer in between).
Use care as the magnet is quite strong and the magneto will be pulled to it with a strong force.
Now firmly tighten the two screws that mount the new magneto and slowly rotate the flywheel to remove the cardboard. Replace the engine top cover and your done.