General Tips:
Some good things to do to bolster your chances, in no particular order:  superb grades, good GRE scores, a high quality proposal,  an Honours project, volunteer in a lab or for a field project, publish a paper on your research, present your research at a scientific conference, present at a student conference,  do an independent studies course, get a good reference from a respected researcher, being organized about program and scholarship applications well in advance.

Finally, don't just take my advice.  Talk to other people about this.  Google it - there are sites that give tips on how to succeed in academics.

Five steps to get into graduate school:
The following outline the steps I suggest will help you get into graduate school. They happen a year in advance! So, if you want to start graduate school the September after you graduate, you need to start on this during the summer before your last year (i.e. the summer between 3rd and 4th year). However, you can also delay - you do not need to start graduate school directly after finishing your undergraduate. In fact, if you can gain research or other useful experiences after graduating, it may be helpful for your graduate school career.

Step 1.  Decide on an interest area, and a possible project or two: August or earlier
This helps when you approach supervisors, and also you can use it for your NSERC proposal.  In neither case is it critical that the project be what you actually work on in the end.   The key in both cases is to demonstrate that you have independence of mind to think things out thoroughly on your own, understand the scientific method, do some background research on previous work and possible methods, etc.

Step 2.  Find a prospective supervisor, and have a conversation about joining their lab: August or earlier
You can find them by reading papers, looking at faculty web pages, and talking to mutual connections This can be the hardest stage... talk to many people about this.  Once you've got a name, the first approach should be a brief courteous email with a few ideas on what you might work on.  But not the full length proposal. That can come later, once it looks like there are possibilities (the conversation may be cut short if they are going on sabbatical, have no grant money, or already have a full lab).   Busy people don't always read long emails!   The best approach is to look several at different schools and supervisors .  This is entirely legitimate - you can have several places you are thinking about going.

Step 3.  Proposal: late August/early September
Once you've got a prospective supervisor(s), refine one of your project ideas into a good proposal for NSERC.  Get feedback from faculty and grad students who've gotten NSERC money before.  I would suggest at least 2 different people.  Make sure you polish it before getting feedback - good grammar and flow mean the feedback will focus on the science.  Badly polished english will simply distract people giving you feedback and (ultimately) annoy the NSERC committee judging your application.

Step 4.  Nail your NSERC application: mid September, to allow time for reference writing and mailing
Read and understand the instructions and tips on the NSERC website for the various different types of awards.   Go to the information sessions NSERC always holds in the fall at canadian universities.  Ask questions about bits that are unclear.   Get feedback on the various free form components where you talk about why you are going to be good researcher.  Get your application all together with plenty of time to send to your referees.  They need a minimum of 2 weeks to work on it (i.e. between receipt of your materials and the deadline by which they have to return stuff to you).  Consider providing self-addressed ExpressPost envelopes for them to send the references back to you (this can also help track whether they have sent them!).

Step 5.  School Applications: October and later, depending on application deadlines
Submit your grad school applications to the schools you've talked to supervisors at.  Again, any free form components should have been carefully written and editted with feedback from another person.

Possible Extra Step.  Complete the GRE: October or earlier, to allow time to receive your scores before program application deadlines.
Most (all?) graduate programs in the USA, and some in Canada require the GRE general test and some also require GRE subject tests. Programs that require these will have minimum scores you must achieve, although, higher scores can improve your application. Intensive studying and practice exams can greatly improve your performance on the GRE tests. Start studying early - at least 6 weeks or more before your exam date (i.e. August or earlier!).