Animations like that are usually made using cel shading combined with hand-painted elements. This effect is known for quite some time, occasionally it was used even in real-time rendered computer games (eg. Borderlands). Major difficulty usually comes in combining style of hand-drawn elements with 3D renders in a way where everything is consistent.
As for animation style - cel shading doesn't differ from anything else. It's just specific type of render. If you know how to correctly rig and animate character in cel shader - you know how to do it in any other render style. It's more about mastering 3D software then learning one specific animation style.
All the animated stuffs were made in 3D (with painted textures), but the backgrounds are in 2D.
", and "we used 3DsMax for this production
". Why not ask them and direct them here? :) would love to see a more detailed description, it's a great style done really well – user56reinstatemonica8 Jan 31 '14 at 9:42