I filed a paper federal extension with zero taxes due. I did not use turbotax to file the extension. How do I input that I filed an extension in turbotax?

You don't need to enter or report an extension.  Just efile your return.  You can efile until Oct 15.  Did you make a payment with the extension?

To enter the amount you paid with an extension (including state extension)  go to

Federal Taxes (or Personal for desktop H&B version)

Deductions and Credits

Then scroll way down to Estimates and Other Taxes Paid

Other Income Taxes - Click the Start or Update button

Next page second section Payments with Extension

Either Visit All or Click Start or Update by the extension you paid

Turbotax doesn't need to know that you filed an extension, it only needs to know how much estimated tax you paid with the extension (which you enter as directed).  If you didn't make an estimated payment, you don't need to do anything about the extension.