It's pronounced "bah-nhay-ro", with the stress on the second syllable.
However, you might also hear these words used:
* "Casa de banho" (literally "house of bath") - more common in Portugal.
* "W.C." - abbreviation for "water closet", mostly used in Brazil.
* "Toalete" - more formal and less common than "banheiro".
It's always helpful to use the context and the region you're in to determine the best word to use.