Where do enter the 400.00 that Arizona allows as credit if you donate to school

To enter information for Arizona Form 322 (Credit for Contributions Made or Fees Paid to Public Schools) in TurboTax, please take the following steps: 

1. Select State Taxes tab
2. Select your Arizona return
3. Verify the information on each screen in the Arizona interview section for income and deductions as it is displayed, then click on Continue button
4. When you reach the "Contributions, Tuition and Fees Paid to Qualifying Schools” screen, select "I paid fees or made a contribution to an Arizona public school by April 18, 2017 (not already claimed on my 2015 return) to support extracurricular activities that I wish to include on my 2016 return" and/or "I claimed a credit for contributions or fees paid to public schools in 2015 or a prior year 
   that was carried forward to 2016", or either of the same selections, but for a private school
5. You will now be able to enter your Form 322 contributions and prior-year carryovers (if any)

More information about Arizona school tax credits is at https://www.azdor.gov/Portals/0/Brochure/707.pdf

I was able to enter this in my AZ state return. Does this amount need to be entered somewhere on my federal return as well? If so, where would I enter that? I don't want to get in trouble if I entered it on my federal and state and and was no supposed to. Thank you.

No, it does not get entered on the Federal return. It is a state credit only.