If you are a dependent of your parents, they would claim your exemption, education expenses and payments.
(be sure to elect "Someone else can claim me" during your personal info interview)
If you are not a dependent, and you are claiming your own exemption, whatever someone paid towards your education expenses are treated as if you paid them.
CLICK
HERE for IRS Pub 970 Tax Benefits for Education
CLICK
HERE for TurboTax help on Rules for Claiming a Dependent on Your Tax Return