This might sound like a cop-out answer, but there are so many ways to handle the mouth, and the best method depends on the character design and how it will be animated. I suggest experimenting and finding what works best for your situation.
For me, I usually place the mouth in a Switch Layer and use the same switch for the range from front to front 3/4 views. To do this, I place each mouth pose inside its own group and break it apart into layers, typically Mouth, Teeth, and Tongue layers. Then, in the Head Turn Smart Bone Action, I'll slide the position of the teeth and tongue to the left or right to give the inside of the mouth depth. Also, I might reshape the edge of the mouth to give it dimension as it slides into its 3/4 view.
There have been times when I rotated the Switch Layer group on its Y-axis to give the drawings a cheated perspective in the 3/4 views. This works great, but you need to remember what's going on if you need to edit it later. (Actually, I guess the perspective is real, and what I've cheated is the drawing.)
To be clear, I use the same Switch from 3/4 left to front to 3/4 right views and animate the angles (shapes and perspective) in the transition. But when the character is in full profile, I'll use a different Switch Layer with side-view versions of the mouth poses. This lets me use a different setup where I can cut out the shape along the side of the head.
I may even set up a mouth control that keeps all of the mouth Switches in sync. That's really not necessary, though. In fact, these days, I like to use the Switch Selection window instead of a Smart Bone to animate mouth poses. This method requires very little setup, is easy to animate with, and lets me smoothly interpolate between mouth poses. (This Switch Layer sub-interpolation won't work with a Smart Bone.)
MrMiracle77 mentioned using a mesh warp, and I agree this is another good method. To do this, make sure your vector shapes have the points to support the mesh warp. Tip: controlling Bezier Points can get funky with this level of warping, so I usually reset the curvature in the curves and disable Bezier when I know I'll be doing this. The curvature will deform more predictably this way.
So, yeah, lots of different ways to animate mouths, and the above are just my personal go-to methods.
(As for tutorials, I have something coming in mid-June, so stay tuned. But don't tell anyone...it's a secret.)
