Before opening up Illustrator start with a quick pencil sketch. We're going to use the Pen Tool to trace over the lines to give the cartoon a polished feel. The sketch doesn't have to be perfect, it's just a point to work from.
Import the scan onto the artboard and then set the transparency to about 25%. The transparency makes it easier to see the lines you're drawing on top of the sketch.
Before we start tracing, we're going to create a set of brushes that will give the outlines a more traditional ink look. I used the Pen Tool to make some shapes that look like rough lines. The width is varied in spots to give the strokes a personality.