Start with the waitlist, but do not stop there
Add yourself to the electronic waitlist immediately (position is by time). Then work the other angles in parallel, because the waitlist alone may not clear in time, especially for a small or high-demand course.
Email the instructor
A short, specific message: your name and ID, the course and section, why you need it this term (a prerequisite chain, graduation, your major sequence), and that you are on the waitlist at position N. Ask whether they are able to add students or issue an override. Instructors often have some discretion, particularly for majors and seniors.
Ask the department
The department office or the undergraduate coordinator handles seat requests, permission numbers, and decisions about adding a section. Tell them your situation. If several students need a course that is full, that is exactly the information that leads to another section being opened.
Attend the first class
Show up to the first meeting even though you are not enrolled. Tell the instructor before or after that you are waitlisted and hoping for a seat. Registered no-shows get dropped in the first week, and instructors commonly fill those seats with the waitlisted students who are in the room.
Look for alternatives
Another section, the same course at a different time or campus, the course offered next term (if your timeline allows), an approved substitute course, or the same requirement met a different way. Your adviser can tell you which of these actually keeps you on track and which just looks equivalent.
What not to do
Do not assume you are in because the instructor said "probably" — get the registration confirmed in the system before the add deadline. Do not stop attending a waitlisted class while you wait. Do not let the add/drop deadline pass without a confirmed schedule that keeps you full-time.
Fictional information
UW–Porter Falls is a work of parody. Every office, person, building, phone number and statistic on this page is invented; nothing here describes a real institution or a service you can actually contact.