How do you distress a beige chair?

Since the chair is already light colored, when you start distressing, there won't be much color difference to be noticeable. First try sanding a little bit for the wear effect, and see how it looks. If no good, then repaint the chair a darker color, such as a darker brown, and try the distressing again.

Are you asking how to distress too? Usually it is by sanding areas that would naturally get worn off, plus lots of people hit the piece of furniture with chains or hammers, etc. to give it a "used" look.