The first step to getting a good render is having a good character design. This begins with color concept art. This communicates what the model and textures should look like.
Image credit: Ember Labs (Click image to enlarge)
The next step is to turn that concept art into a model. The model should follow the concept art (as the above example shows). Regardless of the look you want to achieve, a quality model is essential. You need a nice model to get a nice look, just like you need quality ingredients to cook a quality meal.
Render Looks
Feature Film look
If you want to go all out, you can go for the look you see in feature animation films by Pixar, Sony, Disney and others. This means all the bells and whistles: hair, sss, cloth sim, HDR.
Here's an example of that look from SHED, including a side-by-side comparison with the animatic (top left), layout (top right), animation playblast (bottom left), and final render (bottom right):
Beautiful but hard. You'll need a team of lighters for this.
Beware of the "cartoon look"!
Let's assume you want to do a simple look so you can focus on animation. A common mistake students often make is assuming that a hand-drawn cartoon look is simple. When working in 3D, a hand drawn 2D cartoon look is not easier to do, it is much much harder. This is because it means you are asking the software to do something it was not designed to do (looking like a two dimensional drawing). On top of this it requires that you can do hand drawings and paintings. If that's your thing, great. But if you are trying to do something simple this is the opposite of simple. So if your goal is to try to keep things simple, this is not the way to go.
A classic example of this style is the animation short Meet Buck:
Looks simple, but this look takes a LOT of time.
Animated TV Series Look
So how can you get a simple look? A good approach is adopt the approach used on animated TV shows. In a nutshell this involves combining flat colors with ambient occlusion. This can then be augmented by a colored light and shadow (for example yellow sun light and sky blue shadows). If that's too technical, don't worry. You'll learn about this technique in the class Fundamentals of Texture & Light.
The main thing to get is what it looks like. You've seen this look in tons of animated television series. They use it because they have a tight turnaround time.
Here's an example of it from the TV series The Garfield Show:
Setting up the Animated TV Series Look
The "Animated TV Series Look" look is done by assembling the lights in the comp. That means instead of doing the lights in Maya where we need to wait for a render, we instead make them in comp which we can tweak in real-time.
For this setup you will need three things: A flat texture pass, ambient occlusion, and a raw light pass, as seen here:
Flat texture pass You can create the flat texture pass by assigning Surface Shaders with either a color or texture in the color slot. This is equivalent to the "diffuse" pass in Vray or the "Diffuse Material Color" pass in Mental Ray.
Ambient Occlusion I'll assume you know how to make an occlusion pass.
Raw light A simple way to make the raw light is to create a render layer with a white shader assigned to everything, which is then lit by a single light. This is the equivalent of a "raw light" pass in Vray.
With these three passes we are ready to built out lights in comp.
1. First we multiply the textures with occlusion:
Textures x Occlusion = Occlusion result
2. Next we multiply that with the color we want to have in the shadows. This gives us our indirect light:
Occlusion Result x Color = Indirect Light
3. To create the key light we multiply the occlusion result we made above with a raw light pass. When combined in the comp with our occlusion result, this gives us our direct light:
Occlusion Result x Raw Light = Direct Light
4. Finally we add the indirect light and the direct light together for our final look:
Indirect Light + Direct Light = Final result
We can tweak the colors live in the comp to get whatever mood or light situation we want, and even quickly render a different raw light pass if desired. You can of course also add extra things like glow effects in the comp too.