It’s pronounced DO JAY and, from 697 a.d. to 1797, this figure was the supreme magistrate in Venice (Genoa also had doges).
The word itself comes from the Latin dux (meaning commander or general). He was elected for life, and was usually elected during his golden years, so that “elected for life” didn’t actually mean a long time.
The corno ducale was the sartorial and visual confirmation that this man really was the commander in chief. This corno ducale was a hat, quite like a skull cap, with one horn on the left side. How to address the doge? “Most Serene Prince” would do, as well as a simple “Your Highness.”