Once you have located a relevant community association, locate their website to get an understanding of the work that they do and the communities they serve (hint: look for the About Us or Contact Us page). You can then follow up by email with an inquiry to get more information.
Major urban centres will frequently have websites that list culturally specific organizations, for example, the website BlackMontreal.com. It's worth some targeted Googling (i.e. "Brampton Punjabi association" or "Scarborough Filipino association") to locate something similar in the geographic region you are researching. Some of these associations may be focussed on a specific issue such as health, and you can add a specific keyword to capture that (i.e. "Scarborough association health"). You could also encounter organizations such as food banks that serve very specific communities; try a search for "Halal food bank [geographic area]".
Local BIA (Business Improvement Associations) may also maintain lists of businesses run by specific cultural groups. Often, these directories will also come from the communities themselves, for example, Shop First Nations is a directory of First Nations, Metis and Inuit owned/operated businesses.
Above all, existing relationships within these communities are the best and most authentic connection that can be made; in absence of first hand knowledge, respectful dialogue and questions that are sensitive to the cultural context of the folks being approached are a good place to start.