The "Ye" in "Ye Olde Tea Shoppe" and similar signs should be pronounced "The".
Anglo-Saxon (Old English) had two different letters for the "th" sounds: an eth for the th in that and a thorn for the th in thin .
These were represented as follows:-
eth
thorn
The eth died out in the 1300s, and the thorn was finally replaced by the th (called a diagraph) in the 1500s, by which time it had come to look very much like a y. For convenience some printers actually used the letter y.
People eventually forgot what the thorn meant and interpreted Ye (the) as Ye (ye) when they saw it on old signs.
