The most common way of saying goodbye in Spanish is "adios." Adios comes from the word "a," which means "to," and "Dios," which means "God". So, "adios" means "to God."
If you want to say, "Until we see each other again,", say "Hasta la vista." The phrase got some extra traction from the "Terminator" movies. The "v" sound is more like a "b," so this is pronounced more like, "Hasta la bista."
"Hasta ahora" means "we'll see each other in a while," and "Hasta mañana" means "until tomorrow." Both are common ways of saying goodbye at the end of a day.
"Nos vemos" means "we'll see each other" and is used casually like the English phrase, "see you around."
Say "me voy" for "I'm leaving now" and "Me despido" for "I'm saying goodbye." "Que te cuides" means take care, and "chau," which appears in other languages, simply means "bye."
