Italian pronunciation:Jiyoo-Lee-Eht-TahPicture the "Giu" to the first to letters of the name "Judy." Now, add emphasis and individual distinction to the first three letters, "Giu," until it basically comes out as a very soft "Gee-Oo." "U" as in "Rude." Stress "I" into "EE." "E" turns into "Eh," or otherwise a near "Aye" sound. Both "T"s are pronounced noticeably to Italian speakers (they make sound as one to English speakers, however). Most easily accomplished by placing extra emphasis on the letter before (in this case, "E") and continue onto both "T"s. "Ta" equals "Tah."
The first syllable is pronounced just and simply "joo", certainly not "gee-oo" with emphasis, individual distinction or who knows what. The real pronunciation is joo-LYET-tah, and any Italian could confirm.
Adding to the above comment about Fellini, the title character from the movie Juliet of the Spirits takes its name from Fellini's wife and partner, legendary Italian actress Giulietta Masina, who plays Giulietta (or Juliet) in the movie. She stars in many of his other movies, including La Strada.