Many of the puppets like Ernie are sometimes called Live Hand puppets...because they have "live" hands in place of stuffed ones I'm guessing.
There aren't actually many differences between live hand and rod puppets that have a human body rather than a large open body like Cookie and Co.
The head and torso tend to be exactly the same, the only difference is that instead of having a foam hand at the end of the arm, you attach what looks like an oversized long glove at somewhere around wrist level, so the hand looks like it is attached to the puppet's arm while your hand is hidden by the "glove" sleeve. I'm not sure how clear that description is.
If you do a google search for behind the scenes photos or have a look on you tube at some of the videos you will see it better...particularly puppets like Ernie or The Count. Also, if you watch videos of Ernie you will notice that most of the time you see only his fingertips and occasionally what would be the knuckle area which is basically because if you saw any more then you would see the sleeve that the puppeteer's arm is in. There are some good behind the scenes photos on google of Jim and Frank working Ernie and similar...they will give you the best idea.
There is a pattern for the arms/hands available from Project Puppet, but to be honest, it is a hand shape on the end of an arm sleeve...a bit trial and error will soon lead to a decent hand, and you can always play around with it and add extra fingers or take fingers off etc. Best way I have found is to just have fun with it.