Hi,
1. You can work on campus - this does not require any special process / visa. you'll need to follow your school's regulations. normaly this will require that you have a social security number (you'll need endorsement from your school to get one) and filling tax forms. It's simpler than it sounds.
2. after 1 full academic year in F-1 status you CAN also work off-campus, under certain conditions/programs. There are 3 options: The two normal ones are OPT,and CPT. There's a 3rd option - "special economic hardship".
To learn more about those - see the following 2 links:
http://www.uga.edu/oie/ISSIS/Immigration_Students_Current_Employment_Off.htm
http://www.columbia.edu/cu/isso/visa/F-1/F-1_off_campus_work.html
Good luck!