I am a full time student with tuition expenses on 1098T and my parents are not claiming me on their taxes. How do fill out the form to qualify for the credit?

Since you CAN be claimed as a dependent, you are not eligible for the refundable portion of the American Opportunity credit.  You may only claim a credit if you have an actual tax liability, to offset.

While technically there is a provision that allows a student-dependent to claim a federal tuition credit, from a practical matter it seldom works out.  A student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit (AOTC) if he/she supports himself by working. She cannot be supporting herself on student loans & grants and 529 plans and parental support.  It is usually best if the parent claims that credit.  

If the student actually has a tax liability, there is a provision to allow him to claim a non-refundable tuition credit. But then the parent must forgo claiming the student as a dependent, and the $500 other dependent credit.  The student must still indicate that he can be claimed as a dependent, on his return. This is worth up to $2500 (AOTC shifts to all non refundable)