Graduate students do take courses as well, but courses are subservient to the aim of developing the skills and expertise required to conduct and publish original research. The following are likely to increase your chances of getting into a good graduate program in research-oriented psychology. Majoring in psychology as an undergraduate and taking upper-level courses in the area of specialization in which you want to pursue graduate study is definitely a plus, but not necessarily essential. Get good marks in your undergraduate courses, especially in your last two years. Potential supervisors will not have very much information on which to base their decisions, so marks will play a substantial role.
Graduate study is a full-time commitment.
Some potential supervisors provide some financial support for some students, but such funds tend to be in very limited supply. Unless you are an absolute superstar on every other dimension, your chances of being admitted will increase dramatically if you have your own funding. Producing a strong application will take a substantial time investment, so start early. Get feedback on drafts of the proposal. Applicants with mediocre GREs are less likely to be accepted.