The U.S. Citizenship and Immigration office, which oversees F-1 visa holders once they are in the U.S., states that "work" is any activity from which a person receives material benefits, whether those are money, tuition, room and board, books, etc.
Students on F-1 visas can work at student jobs on the campus at which they study. Student jobs are regulated by labor laws that limit the amount of hours per week to 20 during the academic year (though students can work full time during holidays and vacations). Check with the international student counselors on your campus, but most international students can apply for campus jobs the same as a regular student and do not need special permission or extra documentation.
Students on F-1 visas can also do work deemed curricular practical training (CPT), which is work required by a student's course of study, such as an internship, practicum, research or student teaching. Students are eligible for CPT after they have been enrolled for one year in an academic course of study. There are exceptions for graduate students who can prove that their course of study requires some kind of work prior to the one-year mark.
Once students have reached the limit of their curricular practical training, they can apply for permission to do optional practical training (OPT). OPT is work in which a student applies the theories and training received through an academic course. F-1 visa holders are allowed a year of OPT per course of study but must get permission (either for post- or pre-degree completion OPT) from USCIS before starting an OPT position. Students are encouraged to apply early, as obtaining permission can take up to three months.
Students who experience a dramatic change in their financial status and need to work to support themselves may apply to the USCIS for permission to work off-campus. Students must have been enrolled for a full academic year, be able to prove economic hardship and submit an application with form I-765 to the USCIS. Talk to an international student counselor on your campus before submitting an application.