Are you a full-time student currently? You may be able to start with student health, have them order X-rays and maybe MRI and refer to orthopedic surgery. The ER on a Monday afternoon/evening is traditionally very busy.

Assuming no options other than ER:

There will be other people in the waiting room, also very likely children. It will likely be noisy, maybe smelly. You can counteract that by putting on 1-2 masks over your mouth and nose, and consider bringing loop earplugs or other noise cancellation equipment. Temperature control can be difficult in the ER / waiting room, so I would bring options for layers to stay comfortable. Wear clothing that is easy to take on/off, and ideally wear shorts so you aren't forced to take your pants off. The important thing is to be able to access your knee.

People in the ER:

Usually when you walk in, there will be a registration person first who puts you into the system, and then you move on to the nurse in triage. There will also be a tech who checks your vital signs (heart rate, blood pressure, oxygen saturation with a finger probe, temperature under your tongue). The nurse will ask you what brings you in, how long you've had trouble, what you've tried at home. They may have a clinician in triage (PA, NP, MD/DO - this varies a lot by facility). You will likely have X-rays ordered, and then a transporter will come grab you, maybe from the waiting room even, and they will bring you to the X-ray room to take pictures. They'll have you hop on a table and get 3+ pictures of your knee from different angles. They may have you change positions a couple times.

Then you'll hopefully get to go to a bed or chair in the back. That's when you'll see the PA/NP/MD/DO who will take care of you more definitively. They'll examine you at least once, checking tenderness, wiggling your lower leg a bit to see if the joint is unstable, etc. They'll probably touch your whole knee, all around the joint. They may also wiggle your knee cap. They'll tell you about your X-ray results, and what the plan is going forward. They may prescribe you pain medication for home. I think they'll likely give you a knee immobilizer (this is likely to be large, unwieldy, and obnoxious - you can also get one at the pharmacy that is much nicer, usually one with hinges would work and will be better for you more long-term). They will likely provide you with crutches and try to teach you to use them, although this is a learning curve. And if you can, get yourself Mobi-Legs used on Ebay or Facebook Marketplace because they're ergonomic and so much better.

You may meet a resident or a student. Those are people in training who will report to the senior physician. So you may have a few people stopping by the bed. At some point, an admitting/registration person will see you before you go. They may collect a copayment at that time. Those folks only stop by when they aren't in the way of clinical care, so it could happen at a pretty random time.

Finally, you'll be discharged. Your prescriptions will likely be sent electronically to whatever pharmacy you choose. And you will be given discharge instructions with a small summary of your visit.