I'm not sure if your question aims at Animation alone or you start up with 3ds Max/ Maya from the scratch
But if you are a newcomer ...
I've been working with 3ds Max for quite a while now and I really can recommend the tutorials of www.digitaltutors.com. Unfortunatly they are not free but they cover everything and nearly every Software from 2D to 3D, animation and design and they helped me a lot to get started as they are professionals in that area, comprehensional and also provide all the sources to go through the tutorials step by step and follow a really good guideline. And of course there are a lot of free tutorials on the web.
For the start split your training into the different categories:
1. Learn to use the interface
2. Modelling
3. Rendering
4. Texturing
5. Animation
You can also define your own ones if you prefer.
Anytime you got comfortable with one category step on and what helped me a lot: Find something in your vicinity that suits your experience and try to model it (a vase, candle, furniture). Practice practice practice and soon you will notice that after a while you only need a few minutes to create a 3D object which took your hours before.
Good Luck! 3D-Modeling and Animation is a great field
PS: Just remembered: www.cgcookie.com has also a variety of tutorials with lots of free ones too.
