How do I demonstrate that I read and understood a professor's paper to the professor?
That is why I have decided that I will read some papers of the professors to convince him that I am well prepared to work under him.

I disagree with this advice. I would rather see applicants (especially those with an MS) demonstrate their ability to do research, usually through a publication or a strong thesis. As long as their topic is somewhat related to my research, that would be a stronger demonstration of their potential to succeed in a PhD program. Being familiar with specific papers that I have written is not necessary or expected (you can always read such papers if you are accepted).
If your only option is to study the papers of professors, my advice is to implement the methods discussed in those papers numerically, i.e. repeating the results, or possibly even conducting some trivial yet new extensions (like repeating the experiments on a different dataset). That would be far more impressive than simply reading a paper (where your depth of understanding is not clear).