Browse the department’s program pages and course descriptions to see which faculty members are teaching courses you are interested in. You may want to consider some faculty members as potential co-supervisors or as committee members, rather than supervisors.
Some professors also have McGill webpages or research websites. Follow up by reading some of their articles, books or other published materials.
Once you have identified a potential supervisor and you are ready to contact potential supervisors, approaching them by email is a good initial step. Ensure that your messages are tailored to each professor, not generic. You should catch the interest of the professor quickly and make a good first impression. It is advised that you contact one potential supervisor at a time. State why you are approaching this particular professor, and why your research interests and goals are a good match.
Talking to the current and former students of a potential supervisor is a good way to find out about their supervisory style, and will allow you to determine whether you work in a similar way.