You may work part-time (up to 20 hours per week) on-campus for Columbia from your first semester. Paid on-campus work is an allowed incident to your F-1 status and does not require additional Optional Practical Training (OPT) authorization. To be eligible for paid off-campus work, you must have completed an academic year in valid student status before being eligible. Any paid off-campus work (wages, or other compensation like a stipend or housing) requires authorization through OPT. OPT is approved in your field of study and requires an application to the immigration agency. The ISSO will assist with this. Refer to this summary of employment possibilities.
For unpaid work on or off-campus such as volunteering or an unpaid internship, you may start right away and do not need OPT. You must be sure the position is unpaid for anyone (i.e. not just you because you want to take the job as a volunteer).