Portable dryers work in exactly the same way as their behemoth, non-portable brethren: through the process of forcing hot air to evaporate water in a drum of clothes, rotating in order to prevent wrinkles. Other than the addition of handles, portable dryers are the same, just in a smaller unit.
Portable dryers begin the drying process by sucking in air from outside the dryer, generally using the suction from a fan used to expel air from the dryer. The air is then forced over a heated element, like that in a toaster or a household electric heater, and is heated to a high temperature. The air then gets pushed into the drum, which has perforated sides that allow air to enter and moisture to leave.
The drum spins by force from a small pulley, attached to the drum by a belt. An electric motor drives the pulley, as well as the dryer's single fan, which moves the air in and out of the unit. The drum spins to prevent clothes from settling, and thus forcing wrinkles and creases.
The dryer's lone fan sucks the moisturized air out of the drum and forces it out of a duct, either into a tube hooked up to the outside air, or into the general surroundings.