I'm currently working on an M.Sc., at a Canadian university. To get in, I just had to apply to the department that I was interested in. The application included an undergrad transcript, a description of what I wanted to study, and three reference letters from professors. Choose professors who you have gotten to know reasonably well so that they can actually write something more than ____ was a good student. I actually applied to two different departments and was only accepted to one because the other already had as many grad students as they were taking that year (so apply early!).
It also helps if you are already in contact with a professor in the department that you are applying to. It's even better if you are in contact with a professor who is willing to be your advisor before you apply. An easy way to open up the lines of communication is to send an email to the contact person for whatever department you are considering and ask for some information on graduate studies there. Many departments have websites where they advertise for grad students, listing certain research projects that a professor would like to have done and whether they are at the master's or doctoral level.
Also, apply for scholarships and fellowships. There are some that you can apply for even before you have finished your undergrad degree. It always looks good if you are bringing your own funding with you in the form of a scholarship or fellowship. In order to apply for most of those though, you will need some idea of what you plan on studying. It can be somewhat difficult to know for sure what you are going to study until you've talked with professors and found out what the possibilities are. So your first step should probably be to think about what you'd like to study and then talk to some profs who do research in that area. Networking can only help you
One last thing - while some people do all their degrees at one university, apparantly it looks better afterwards if you have studied at a variety of universities. The best situation is a different university for each degree, with at least one of those universities being in a different country. And as the degrees get more advanced, it's a good idea if the universities are ones that are recognized as quality institutions in your field of expertise. So that's something to consider when choosing a university.
However, I think that the single most important factor for many people is who they get as an advisor. A good advisor or bad advisor can really make a difference in how your years as a grad student will go. The best way to find out about what kind of advisor any given prof is is to talk with his/her current and former grad students.
