This is kind of a late question.
I am contractor at my current job (19 years old) and I have to pay taxes this year. If my parents claim me will the taxes I owe just come out of the money they get back? Or do I still have to send my taxes in?
Yes, you will have to file taxes. Each peson gets a standard deduction. By "claiming you", your parents are applying your standard deduction to their taxes, meaning that you cannot use that same deduction on your taxes. You still must pay taxes on your income. This generally works out best overall, assuming that your parents are in a higher tax bracket (have a higher income) than you.