Q:

How to determine the instaneous rotation axis?

I am not sure if it is ok to ask such simple question.    
I am not the student of physics and am considering the following picture:  

Why is $P$ the instantaneous rotation axis?  To me the point CM should be the instantaneous rotation axis since every point on the wheel is rotating around it.     

It should be like the following:  (instantaneous rotation axis is at the CM)

A:

It's a matter of reference frames. It is true that from the reference frame of the CM, every point on the wheel is rotating in the same direction (and angular velocity) about itself; but it is also true that at the point of contact, every point on the wheel is also rotating in the same direction (though not at the same angular velocity.)
Depending on the problem, the point of contact reference frame may be more convenient for certain calculations. Among other things, it has the convenience of being stationary relative to the ground, which the CM is not.

