Obtain the right kind of adapter. These should be easy to find at an electronics store or at the airport, whether you're in America or Italy when you shop, but not all adapters are the same. The adapter you use needs to have the right plug configuration for the outlets. Most outlets in continental Europe are designed for plugs with two round prongs, so your adapter should have two round prongs, not the flat ones used in American outlets. Each adapter will be labeled with the countries for which it is designed.
Purchase the right kind of converter. There are two main types. One is for motorized and electronic appliances like laptops and radios that run on less power. The other is for running heating appliances like your hair dryer. You'll need a high-power heating converter to power your hair dryer.
Many converters (including most toggle types) are not designed for continuous use. If you're plugging in a laptop, recharging a camcorder or some other device that must be plugged in for a long time, buy a heavy-duty transformer designed for that purpose.
Plug the hair dryer into the converter first, then plug the converter into the adapter. Turn the hair dryer on and use as you normally would.
Unplug the hair dryer when not in use. You should not leave most converters running too long. This is less of a problem for hair dryers, as opposed to laptops or other devices that are typically left on for hours at a time, but use caution.