Isolating transformers work by having a regular step-up or step-down transformer in which two coils of insulating wire are wound around an iron containing core, but it includes a Faraday shield which isolates the coils from each other and grounds the transformer case. This effectively isolates the transformer's coil, protecting the device from grounded objects and protecting people from the dangerous, deadly high voltages.
Transformers themselves work based on magnetic currents. One coil, called the primary coil, is connected to a source of alternating current which produces a varying magnetic field in the iron containing core. This varying magnetic field then produces an alternating current in the second coil, which is connected to a separate circuit. The ratio of the number of turns in the first coil to the number of turns in the second coil, also called the turns ratio, determines the ratio of the voltage change that the transformer provides. Step-up transformers increase the voltage output by having more turns in the secondary coil than in the primary coil. Step-down transformers work in the reverse. Power remains the same through a transformer, and since the electrical power is equal to the voltage times the amperage, the ratio of the change of the voltage through a transformer is inversely proportional to the ratio of the change in the current.