When you're admitted to graduate school, the university will send you a package describing your degree requirements and the details of your stipend. On average, a Canadian graduate student will make 19,000 per year (sometimes less, sometimes more). Your stipend summary will be broken down into teaching assistantship, research assistantship and departmental scholarships. Having a stipend is great. I am ecstatic that I get paid to do Science. But, depending on your student fees, stipends can be eaten up pretty quickly. What can you do about it?
It seems obvious but the best solution is to apply for a lot of scholarships. All universities have an awards and/or financial aid office. You can usually request information on available scholarships or log on to their webpage. In Canada, most, if not all, science graduate students will be applying for funding from the National Science and Engineering Research Council (NSERC; http://www.nserc-crsng.gc.ca/) (for the social sciences there is SSHRC, for the medical sciences there is CIHR). NSERC awards are competitive and applications take a lot of time, so check the deadlines at your institution and start preparing early. Always ask your supervisor for feedback on your research proposal and request reference letters as early as possible (if you request letters the day before they're due, you're liable to annoy your supervisor).
Other Canadian awards include the Queen Elizabeth II graduate scholarships. At some (maybe most?) institutions these applications are reviewed internally so check with your awards office. Many provinces also offer provincial scholarships (Alberta Innovates, Ontario Graduate Scholarship) and most universities offer a suite of internal awards. Your awards office should have information on available provincial and internal awards.
There are also numerous small (and some large) awards available through professional societies including, but not limited to, the Society for the Study of Evolution (http://www.evolutionsociety.org/awards.asp), Society of Vertebrate Paleontology (http://www.vertpaleo.info/Awards.htm), and the Canadian Society of Zoologists (http://www.csz-scz.ca/awards/research_grant/description.html). All major societies offer grants and scholarships but you usually have to be a member. The good news is most student memberships don't cost more then $60 per year.
My biggest piece of advice is to apply for everything for which you are eligible. I have heard many graduate students say they won't apply for certain awards because "they won't get it anyway." Well, you CERTAINLY won't if you don't apply! The more scholarships you apply for (successfully or not), the more experience you gain and the better your applications become. I applied for NSERC three times before I was successful. My proposal improved a million fold from the first application to the third. My experience with scholarship applications has now earned me several competitive scholarships including a Fulbright Scholarship. So keep writing those applications! You're never wasting your time!