This is one of the most common questions I see about Oobi, and about puppet shows in general. How do the puppeteers perform Oobi? Now, I don't know the specifics, but thanks to behind-the-scenes photos I've come across, I'm able to piece together the "Oobi process."
To show all the hands for the different Oobi characters without getting the rest of the actors' bodies in the picture, they build the sets at a height just above the actors' heads, so that they can raise their hands to be level with the sets and their heads/bodies are below the frame. The motions are nice and smooth, so the actors are always standing, with the sets high off the ground. They wear microphones and watch what they're doing on screens.
This is actually the same thing that Sesame Street and other puppet shows do. Oobi is made like any other puppet show, just without the furry puppets!