the correct way
Lies!
While Webster's lists both pronunciations as correct, the word itself is transplanted from Spanish. The Spanish pronounce it "poo", not "pyoo." So I'll stick with the source over you wacky Britons.
(Although, to be technical, Spanish did itself swipe the word from Quechua, the language of the Incas. And if I'm reading the phonology correctly, a native Quechua speaker would actually pronounce the "u" like the "oo" in "book." But since the Spanish already somewhat bastardized the word, I have far too much respect for Native American culture to bastardize it further by jamming an Anglo-"pyoo" on there.)