Federal income tax is not being taken from my paycheck. I earn on average $1000 every two weeks. What should I do?

The first thing that you should do is contact your employer- either the HR department or your manager to find out what is going on.  You will want to make sure your employer has a current W-4 on file for you.  (You should have completed one before you started working.) so that the correct amount of taxes are being taken out.  Depending on your situation- filing status, the number of dependents, etc. you make not have to have withholding done- but you want to make sure so that you are not stuck with a big tax bill at the end of the year.

See Form W-4 and Your Take-Home Pay

Another very slim and very highly unlikely scenario would be if your employer has you classified as an independent contractor.  If you are getting paycheck stubs you should be okay, but if not, see Am I an employee or an independent contractor?