Okay, undergraduate and graduate students with work-study jobs will work part-time on or off campus while enrolled at school.
do we get to work for private businesses?
You might be able to. Some schools might have agreements with private for-profit employers for work-study jobs, but these jobs must be relevant to your course of study.
do we get paid by the hour or a certain amount?
That depends partly on whether you are an undergraduate or graduate student.
Are you an undergraduate student?
no
Are you a graduate or professional student?
I'm a grad student
You will be paid by the hour or by salary depending on the work you will be doing.
who runs the work study service?