I want to start PHD course.

What is the best way for establishing communications with University Professors?

If you live near the university that you want to attend, then I would call and make an appointment to speak with the professor. When you have a meeting, I would also bring your credentials with you as far as schooling that you have had.

If you don't live near the university that you would like to attend, then I would suggest writing a letter, not sending an email to a professor. When establishing communication, a letter is much more professional.

Some universities might have orientation days where you can go and meet professors on an informal basis.