The advantages of a part-time job are more than financial. A part-time job during college will help you by putting experience on your resume. To employers looking at a pool of graduating students with similar qualifications, having previous work experience will really set you apart from the rest. Part-time jobs can also provide you with a break from studying, which gets overwhelming and exhausting if you do it for too long. Just getting out of your room can help a lot. On the other hand, if you choose the types of part-time jobs that are in quiet departments or don't involve much "active time", it can actually give you a great chance to study while being paid to do work.
Disadvantages of holding a part-time job during college also exist, however. You will have less time to study sometimes, as you will be forced to work when you might really need the time. This is particularly problematic during exam period, for obvious reasons. There is also stress associated with a part-time job, and if this spills over into your academic or social life, it can cause problems. Work will also conflict sometimes with class times, field trips, labs, or other scheduled activities. Finally, your social life may be hindered a little by working part-time.
Types of jobs traditionally held by students include tutoring, odd jobs, food service, campus jobs, bar jobs, and more. TA or campus positions in obscure departments where you don't get many visitors are particularly great jobs to apply for if possible, as you can usually use your plentiful downtime to do your schoolwork and study.
If you need the money badly enough, you can hold multiple jobs, but remember that the more jobs you take, the more stress and anxiety will be added to your life. One job may be best, at least to start with, and if you find you have free time, you can increase the number of hours you work. For those paying for college with part-time jobs, holding just one job or working fewer hours may not be an option. If this is the case for you, try to do your schoolwork efficiently, start early, and avoid procrastination at all costs. The last thing you need is to fail in the school you are working so hard to pay for, or to be fired from a job because you're distracted by academic concerns.
Paying for college with a part-time job is certainly possible, and it's a great experience for those students mature enough to handle it (and good enough with time management).