One of the biggest event during your exchange year in the United States is undoubtedly the Prom.
If you're lucky to have gone to other formal dances, you'd have an idea of what Prom would be like; it's basically the same, but only limited to Seniors, Juniors , and their dates. It usually requires a strict formal dress codes.
Prom is a very big thing here; people rent Limousines with their friends, go to fancy restaurants, stay at a hotel, etc. It's basically one of those days you'd remember forever.
Now, you don't need a date in order to go to Prom, but it's always fun to go with someone. So, to start, you ask someone to go with you; it doesn't need to be fancy, you can just casually ask them in person, but if you want to make it memorable, you have to go BIG! if you know someone at the scoring table of a basketball game, ask them if you could use the speaker to ask your date; you can also make a fun little poster sign with cheesy quotes and some gifts for your date (that's what I did; it went well, surprisingly).
Once they accepted, you get started on renting a suit / dress, plan on getting a matching color corsages, bootinears, find someone to drive you to the dance, plan on a little after- prom parties, etc! I guarantee you it's going to be one of the best nights you've ever had!
Make sure you follow the rules/ guidelines and be sure not to break any of them.