Your Briggs and Stratton small engine won't start if there isn't any electrical current getting to the spark plug; the main cause of this is rust on the flywheel magnet. When the flywheel rotates, the magnet on the flywheel rotates past the magneto; this creates a magnetic force field that makes the electrical current that is sent to the spark plug. You will need to clean the rust off the magnet to get you Briggs and Stratton engine to start again.
Park your mower or other machine that has the Briggs and Stratton engine mounted on it, on a level spot. Turn off the key. Pull the cap off of the spark plug. You don't want the engine to accidentally start while you are working on it.
Unscrew the bolts holding the cover over the flywheel on top of the engine. Use the proper sized wrenches to unscrew all the bolts holding the cover to the engine block.
Pull the cover up and off of the engine.
Rotate the flywheel until you see the magnet exposed on the side of the flywheel. Scrub the magnet with the fine grit emery paper. Polish the rust off by rubbing the emery paper side to side in line with the grooves on the magnet.
Reattach the cover over the flywheel.
Replace the spark plug cap.