For years, I assumed it was pronounced as it was written. I would pronounce it as "Yee Old." I was a bit surprised later to learn that I had been wrong.
What looks like a "y" is a written character deriving from the old English letter, "thorn," representing the "th" sound. No, it is not the letter "y," it is the letter thorn. The thorn was commonly used in written English in the Middle Ages and for some time after. That explains why we see it on old documents and even in modern written sentences that imitate historical writing. Other than these cases, the thorn has now almost disappeared.
The thorn originally appeared to be written a bit different than the letter y as it had both an ascender and a descender. In fact, it looked more like a lower case written "p" on top of a lower case "b" than a "y." It typically looked like this: þ. This was before the days of printed books when all documents were written by hand. The exact shape varied from one scribe to the next. By the mid-15th century almost all scribes stopped using the descender, and the thorn has since been written in an identical manner as the modern letter "y."Depending upon the scribe, the second letter was often written above the thorn, as in . Reprints of the 1611 edition of the King James Version of the Bible always show "ye" written as .
While the Middle English thorn is now written exactly the same as a modern letter y, it always was pronounced with a voiced "th" as in "this." In other words, several hundred years ago the word that was written as "ye" always was pronounced as "the," exactly the same as it is today. An educated person of 1611 would always pronounce as "the" although today we might spell it as "thee" when referring to a person, as in "thee of little faith." The word "thou" was occasionally written as .
Wikipedia has a rather detailed description of all this at http://en.wikipedia.org/wiki/Thorn_(letter).
So what killed the thorn? According to at least one source, it was the printing press. Here's a simple but plausible explanation from http://www.h2g2.com/approved_entry/A2922077:
The thorn was particularly popular as a sign for 'th' in Medieval English, but with the advent of printing came a problem. There was no thorn sign in the printing fonts, as they were usually cast outside of England. So, since the sign for thorn slightly resembled the lower-case 'y', that's what was substituted.
The thorn was used in several languages besides English but has since been replaced by other letters in all languages except Icelandic, where it is still used.
So, how do you pronounce the following?
Answer: "The Old Pizza Parlor"