How would you introduce yourself to a person from Italy?

The quickest way is to say:

"Salve, mi chiamo YOUR NAME"

which means : Hallo, my name is such and such

you can also add : "Piacere di conoscerla" (formal) or "Piacere di conoscerti" (informal)
which means "glad to meet you"

"Salve" is easy to use, because it goes both for formal and informal. You could translate hallo with "ciao" (informal) or "buongiorno" (formal). Salve goes either ways.