Before every term, Dartmouth students go through Course Selection to pick their next classes. My parents have talked about their course selection in college before the Internet, where they would wait in long lines to give the registrar physical cards for classes; Dartmouth course selection is definitely very different from that!
Five days before registration opens, the timetable of classes opens to students so that we have plenty of time to pick out our classes. Registration is a weeklong period where students can pick three classes (the standard term course load). This registration cycle, I've changed my mind about a dozen times about classes, and thankfully, you can change classes as many times as you want during registration.
After registration, students receive their class schedule. After that, there is an add/drop period where students can change classes or add a fourth class if they want.
In most classes, preference is given to majors or minors in the subject and seniors who might need the course to graduate for a general education requirement. I've always been able to get the classes I need for the pre-health track or any major or minor classes.
Professors are often very flexible in letting you into their classes if they are popular and filled up. This past summer, I did not get into the "Jewish Jesus" class because it was so popular, and after emailing the professor, she happily gave me instructor permission to enroll in the class.
Overall, in my experience, the course registration period is a pretty straightforward process. So far, I have had no trouble getting into classes I need for my major, minor, or graduation requirements.