As mentioned earlier, 3D is a broad subject, and a typical finished composition will be composed of several - perhaps dozens - of hours of work in an array of skills. What follows is an overview of the subjects you'll need to learn to be a well-rounded 3D artist.
Modeling. Modeling is the act of creating a 3D mesh, whether the end result is a bug-eyed alien or a teacup. How you get to that finished model depends largely on the methods that make the most sense to you.
Animation. Animation is the process of taking a 3D object and getting it to move. Animation comes in a few different flavors. There's keyframe animation, where the animator manipulates the objects on a frame-by-frame basis, similar to hand-drawn cartoons. Other methods of animation include placing objects on splines and setting them to follow the path of the curve, or importing motion capture data and applying it to a character rig. Another way to animate is to use your 3D application's built-in physics engines, such as when your scene requires that objects fall.
Texturing. Without some kind of texture art, everything will be variations of solid colors. The most common and accurate way to create a texture for a model is to "unwrap" the mesh (flatten it out) and paint over it in an application such as Photoshop. The final texture is then "wrapped" over the original mesh again. Depending on how a model is created, each section may have its own texture, i.e., a separate texture for hands, one for arms and one for the torso of a character, all made to blend together seamlessly.
Rendering. Rendering an image is typically the last step, and is perhaps the most important part. It's often overlooked by beginners, who are more focused on creating models and animating them. There are many aspects to creating a good final render of a scene, including attention to camera placement, lighting choices which may affect mood, shadows, reflections, transparency and the handling of special effects, such as fluids or grasses.