How we can look active both in class and after class in our supervisor's mind? I have started my master's degree and I am a fully funded student. 
I want to get perfect marks and do my research perfectly.
What steps should I follow to become an outstanding student in my supervisor's mind?
How can I be a perfect student?
I also have a class with him this semester. I am also doing research with him.

It really does matter to me to have a very good relationship with my supervisor.
Please, give me any advice that you think is useful.
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.