Take a look at many of your favorite characters and think about what you like about them. Some important things to take note of:
- How many heads tall are they? A fewer heads tall character has a proportionately bigger head and a smaller body.
- How are the facial features drawn? The spacing and style of eyes are very important and particular. Jim Henson would let other people construct the bodies of puppets, but he wanted to place the eyes himself, because he understood the importance and particularity!
- What level of detail is there in the design? It can be very simple, like Mario or even simpler like Kirby, or it can be a more ornate design. More details result in a greater degree of design "noise". This obviously varies from character to character but the average amount of noise per character will change depending on the art style you pursue. Figure out if you like characters with lots of noise or smaller amounts of noise.
- Google up color theory. Try and learn a little about it. For a quick fix you can google a color scheme generator. Once you have your colors, try to stick to those colors for your design. Generally I think designs visually make more sense when they use fewer colors. I think the very limited palettes of NES sprites are a good example of limited color selections helping to create memorable and iconic designs- many characters were limited to a mere 3 colors.
There are some places to start developing a sense for character design.