How they make a cartoon in Maya is not too special.

They model and animate the characters and the scene in Maya and then render it (often with thier own custom renderer) so it takes on a 2D or cartoon style.

Some cartoons only have the background done in Maya while some only have the characters (rarer), and then mix it with drawn content to get the final result.

As for dockode's question, I know that some bits of Futurama is done in 3D, but I have no idea wether it is done in Maya.