The parts in a hair dryer are subject to dust and high heat during the natural course of operating. So it's no surprise that those two troublemakers are often to blame when a hair dryer runs poorly or stops altogether. Often, all it needs is a good cleaning and lubrication.
Disassemble the housing, using a screwdriver.
Clean the heating element. With tweezers, extract any hair or lint, then use an old toothbrush to remove dust.
Clean the inside and outside of the intake vent and filter, using an old toothbrush to loosen the grit, and a vacuum with crevice attachment to remove it.
Vacuum the rest of the interior, including the fan, motor and switches. Use the tweezers to remove any hair that's wound around the motor or other parts.
Spray the switches with electrical-contact cleaner to remove grit that may be preventing them from operating correctly.
Oil the bushings at both ends of the motor with one drop of machine oil.
Reassemble the hair dryer.