How we can look active both in class and after class in our supervisor's mind?
Try not to "show yourself as an active student", be it! There is really a difference in it. 

As an active student, you are genuinely interested in the field, you are asking question no mtter how stupid they seem, you are going an extra mile in assignments, be helpful to others (even if no one notices it), be active in students activities, ... 

In fact there are way too many things you could do to do them all. So try to be you and pick what's best for your personality. Then you will shine.