Q: How does a Gentile properly greet a Jew during Passover? That is, what is an appropriate non-ignorant acknowledgment of this observance?

A: Sundown April 19th to sundown April 26 or on the Jewish calendar 14 Nissan to 22 Nissan. This is the offical holiday but preparations for Pesach start several weeks in advance of the actual 7 day period. You can always just say "Happy Passover" or "Happy Pesach". "Chag Sameach" is used for most holidays (translated roughly is have a happy festival) and is also appropriate. In Yiddish you can say "Zeisen Pesach" which is pretty much "Sweet Passover".