In a previous post I covered the characteristics that are important for success in graduate school (http://evolbiology.blogspot.com/2012/10/graduate-school-part-i.html). However, deciding to attend graduate school is only the first step.
It is of paramount importance that you be interested in your graduate research project. Hopefully, you will have some idea of the area(s) that interest you from your undergraduate courses. As a fourth year undergraduate, I knew I was interested in functional morphology and evolution (thanks to some of the really awesome zoology courses at the University of Calgary). But it can be difficult to judge whether or not you will enjoy scientific research. It is therefore important for most fourth year undergraduates to undertake a research project. Usually, undergraduate research projects last two semesters and can give you a taste of your future in graduate school. You can also volunteer for different labs in your department. Most PhD or MSc students would be excited to have a helper (it gives them more time to drink their precious coffee!). Ask to volunteer for a variety of labs doing different types of research. In Canada, you can also apply for summer internships through the National Science and Engineering Research Council of Canada (NSERC; deadlines for undergraduate applications are usually around December so check with your department). These scholarships look excellent on a CV and provide you with unparalleled research experience. It is also important to peruse the recent scientific literature and/or join a discussion group or club.
Solidifying your interest in science might seem like a lot of work. But doing the work is worth it. Graduate school requires a lot of time and mental energy. Being interested in what you do, makes your job fun. Hating what you do, can make graduate school a bitter experience.
Once you're certain that you definitely want to attend graduate school, you need to find an appropriate supervisor. The best first step is to ask professors with whom you are familiar about potential supervisors in the field. They likely know many people and can point you in the right direction. You can also search university websites. Most professors will publish a description of their research online along with a list of recent (hopefully!) publications. I recommend reading some of their publications. This will give you a good idea of their research interests and make you look keen when it comes time for meetings/interviews.
If you can, it is also a good idea to speak to graduate students. Most graduate students will give you their honest opinion about their adviser. After all, you don't want to end up working for someone who is never around or treats their students poorly. You'll be working under your adviser for years (2-5 depending on your degree level) so it's important to at least get along with them.
The next step is to contact potential supervisors. To get the ball rolling, an email is usually best. Be sure to make your email sound professional. Avoid spelling mistakes and don't use "LOLspeak" ("I can haz masters degree?" = BAD). Also, DO NOT send mass emails to professors. Many profs receive hundreds of mass emails from prospective students every year and yours is liable to be ignored.
I also urge you to start contacting people EARLY. If you're emailing professors 2 weeks before the application deadline, you are likely to miss it. Professors are busy people! That being said, I would give them 2 weeks to respond before emailing them again (others might have different rules, so ask around). It is okay to remind a professor of your inquiry. It's possible that they tucked the email away for later and forgot about it. I'd forget emails too if I had several graduate students vying for my time, was teaching courses, and serving on departmental committees (among other things!). It doesn't mean that aren't interested!
Once initial contact has been made there are a few options for how to proceed. If they are at a nearby university, you can suggest a one-on-one meeting. These are great because you can often meet lab members and tour the facilities. If they are far away, it's a good idea to arrange for a phone meeting. They are less personal but will show that you're serious about applying. The professor will usually indicate during the one-on-one or phone interview whether they encourage you to apply.
In the event of a positive response, it's time to apply! University websites usually have good instructions and administrative staff that would be happy to help out.