Im considered a full time college student, and have recently been offered a job. However this job would require me to file a 1099 form. I also live at home with my parents. They are planning like normal to claim me on their tax forms. If they do so will I still be required to pay my taxes that I owe, or being that I am a student do I not have to pay any taxes?

First - you don't "file a 1099 form." I assume what you mean is that you will receive a 1099 form from an employer, and hence you will have to file a 1040 income tax return.

The answer is yes, of course - students work all the time, and file income tax returns as well. You can still be claimed by your parents as their dependent as long as you meet the criteria (you must not provide over half your own support, and you must be under age 24 if a full time student). When you complete your tax return next year you check off a box that indicates that you are being claimed as a dependent by another.