Say "addio" as a general, somewhat informal way of saying "goodbye." The word is pronounced "ah-di-OH" with the accent on the final syllable. This form is used in situations where you would say "'bye" in English.
Use "arrivederci" when you would use the English word "goodbye." Pronounced "ah-riv-ah-DARE-chi," with the accent on the next-to-last syllable, this is the formal way of saying "goodbye."
Employ the informal term "ciao" when you are speaking with family or friends, in a situation where a formal "goodbye" isn't necessary. The pronunciation is identical to that of the English word "chow."
Tell someone that you will see them shortly with "a presto." Pronounced "ah PREST-oh," with the accent on the first syllable of the second word, this is an informal goodbye akin to the English phrase "see you soon."
"A piu tardi" is another informal goodbye akin to "a presto," but with the connotation of, "see you later" rather than "see you soon." The phrase is pronounced "a pyoo TAR-dee."