Today's small engines contain a solid-state ignition armature mounted adjacent to the flywheel. The only moving parts in the system are the magnets mounted in the flywheel, which interact with the armature to produce electrical current. Most ignition armatures are designed to be replaced, not repaired, if they fail. If yours is one of the early solid-state ignition armatures (manufactured by Briggs & Stratton through 1982), it may have replaceable parts. But you'll probably find that replacing the armature is the easiest solution if it fails. A great source of information regarding ignition testing can be found on our Ignition System Theory and Testing FAQ.
Most engines built through the early 1980s contain a set of mechanical points, known as breaker points, under the flywheel. The points open and close an electrical circuit required for ignition. You can improve the reliability of such an engine, if it's a Briggs & Stratton, by bypassing the breaker points system using a solid-state ignition retrofit kit. It's an easy modification.
Before you replace a suspect ignition armature, always test ignition with a spark tester (see "Servicing Spark Plugs"). Check for faulty electrical switches that could be the source of the problem (see "Braking System").
This section covers the procedures for replacing the ignition armature and bypassing a breaker points system with a solid-state system.