Some principle rules to follow with any style is having a base understanding of the head's forms.
Eyes are spheres. Eye anatomy in 2D is basically a circle with a circle at half size in its center (the iris), then the pupil is the smallest and darkest circle (because the pupil is a hole.) Notice how someone's eyes widening can be exaggerated by showing the whites of the eyes more. This expression can invoke a lot depending on context as well as mouth and brow gestures. So, more white shown can express shock, fear, surprise, joy, or something intense like focus or incredulity.
The more "cartoonish" the style, the more you can get away with exaggeration. Don't be afraid to add lines on your faces--this is a great way to show the head's forms, which in turn help you express emotions in your characters.
On your face right now, your character has no lines for eyelids, which can distinguish how high a brow is lifted, or show how bored or tired a character is, or even what direction they're looking. Think about adding eyelids, as it can help with more nuanced expressions. Your character also has no lips, just a line to symbolize a mouth. Think of adding a line under the mouth line to represent a lip--which in turn can help with more expressions.
The chart that @justincarbunkle brought up shows some great examples of cartoon exaggerations. There is always a squash and stretch with expressions--some showing more lines than others depending on what muscles are being used.
Keep it up! :}