It is best to address the professor formally, using their title and last name (e.g. Dr. Smith). If you are unsure of their preferred title, you can use "Professor" or "Dear [Professor's Last Name]". Avoid using their first name unless they have explicitly asked to be addressed that way.
Your email should include a brief introduction of yourself, your academic background, your research interests, and why you are interested in working with the professor. You should also attach your resume and any relevant academic transcripts or publications.
It is generally acceptable to email multiple professors at once, as long as you personalize each email and do not send a generic mass email. However, keep in mind that some professors may prefer to only be contacted individually.
You should try to email professors during the academic year (September-May) when they are actively teaching and conducting research. Avoid emailing them during school breaks or holidays, as they may not check their emails regularly. It is also best to email them during weekdays, as weekends are usually reserved for personal time.
If you have not received a response within a week or two, it is okay to send a polite follow-up email. However, do not email multiple times or pester the professor for a response. They may be busy with other commitments or may have already filled their graduate positions.