Getting started in learning 3D is no easy task. With the advent of widespread gaming, schools have been popping up to teach the different aspects of 3D animation. There are several roles within the Video Game and Film industry. Among these roles are:
-Technical Artists / TDs
These roles also have sub-roles in which are more specialized in the film industry. There is also a role known as "Generalist" which is someone who knows a little of everything.
So, once you get the 3D package of your choice, please remember: 3D won't guarantee you that everything you'll make will be a work of art. Without the basic 2D and 3D (sculpting) fundamentals, it will become harder to create great works of digital art. Please keep in mind that 3D is just a tool, as much as a piece of paper and a pencil are.
If you want to learn to become a modeler, then one should learn more about sculpture, and how molding volumes down to specific shapes can lead to great looking characters or environments. If you are interested in this field, you should look up: polygonal modeling, NURBS modeling, sub-divided surface modeling.
If you want to be a texturer or a lighter, then the basic understanding of how to work with 2D images is needed, along with some basic knowledge of photography. If you are interested in this field, do some research on: painted textures, procedural textures, shaders, and UV mapping.
Animators are hard to come by and are very well respected. It definitely takes time and patience to learn 3D animation. Some resources and topics would involve looking up traditional 2D animation, as well as timing, and acting.
The technical artist or TD is a puppet maker, script-maker, and tools programmer. This is more of a technical job. The main responsibility for someone in this field is to be able to understand the inner workings of the package itself. Some topics of interest would be: rigging, skinning, and MEL scripting (if you are using Maya).
In the field of 3D animation, there are several different fields of study. It's hard to encapsullate just one group of people as 3D animators, since there is so many people behind the scenes of all CG work.