Decide what you are going to draw. Humans, animals, fantasy creatures? Realistic, cartoony, manga, anthro, chibi, and so on. You can draw similar to your favorite cartoon, but don't copy exactly.
Look at your favorite artists, whether they are on TV or on DeviantArt. To get some creative juices flowing, try copying their painting style once or twice in a couple of sketches. If you like how someone draws their eyes, it's okay to draw eyes like theirs. But make sure you don't completely copy their style. They worked hard to find their own drawing style, and so do you. You don't want to commit plagarism.
Create some characters of your own. This will help you. Make them unique as possible - that means no copying your favorite artist! Start drawing them often and maybe you'll develop a new style. Another good exercise is drawing yourself. Most people see themselves as they want to be seen, therefore, if they think they're cute, then they may bug the eyes a little bit, or if they perceive themselves as fat, they may draw themselves lanky. Trying drawing yourself and your perception of how you look, and then branch an art style off of that.
