I was offered some money on my financial aid under “federal work study.” If I accept, would that mean I’d have to work for the school? How does that work? Since I am offered the money, by accepting do I have to work for them?
Here: https://studentaid.gov/understand-aid/types/work-study/
TL;DR: Federal Work-Study is NOT a guarantee of a job, it’s just a guarantee of wages as long as you work the necessary amount of hours in a FWS eligible job. The money doesn’t go towards your bill but into your bank account, so you’ll still be accountable for the remainder of your bill. Your school’s FA Office will be able to provide further information about the program, so check out their website/contact them! 
If you are eligible for work study, it means that the government will cover your wages, but you have to interview for any available jobs, on campus, that are “work study”.
Sometimes the jobs are full. Sometimes, the school does not have any jobs available. It depends on your university.
As you work, you will get a paycheck. It’s not a lump sum that you get at the beginning of the year.
You don’t have to accept work study. It’s offered to you.