On Friday, Matthew's daily calendar of "random things people say incorrectly and how to correct them" (a wonderful gift that we really enjoy, because we are nerds) addressed this very issue!
Here is the answer:
"Yea" is a very old-fashioned, formal way of saying "yes," used mainly in voting. It's the opposite of-- and rhymes with--"nay." When you want to write the common casual version of "yes," the correct spelling is "yeah" (sounds like "yeh"). When the third grade teacher announced a class trip to the zoo, we all yelled "yay!" (the opposite of "boo!"). That was back when I was only yay big.
Thank you, nerd calendar. And Katrina, for knowing us for who we really are.