Very nice, happy dude.  Isn't there an rule that foam puppets usually have 4 fingers instead of 5? We used T arm shirts for human arm puppets where the human's elbow connects to the puppet's elbow.

Do you have any pics? From what I can gather from Ernie, for example, they attached the glove where the wrist would be. I might be misreading it though...

Looks like the puppeteer joins Ernie from the elbow.

Joel is correct that the elbow is where you would enter the puppets lower arm and then into the glove. The top part of the arm is stuffed.  Often on a puppet like Cookie monster the body it is a bit different and more of a wide triangle with the hands at the bottom of the triangle so  you are entering the hands kind of from below the puppet.

Found a few examples for you in the Gallery.  Actually the first one I found was a bit how you envisioned it instead of how Ernie is done.



This second one is like what I explained Cookie Monster would be. Ok so maybe not quite a triangle.

I have used the second method on a monster puppet, but he only had one arm, I made a long glove for him to have a second hand when needed, but it isn't attached.  I guess it all depends on the look you want and how you want to use the puppet.
But you could take a regular shirt and make it work without having to make a whole new shirt.

Creative Ministry Solutions has a pattern for Human arm, T arm shirt.

http://www.creativemin.com/product/566/puppet_building#