Hope you all are doing well...
To approach a professor you should mail them about your interest to work
1. Tell them why you are interested in their research field.
2. If you have any experience or publication related to the research area you
should mention that.
3. Attach your CV, Transcripts, Paper and website link in your mail.
4. Keep the email brief.
Thats all I could remember for now..You can also tell the professor if he
did not accept you, you will kill him in your dream..:P
Hope that helps..