Where do I enter tax payments (state & federal) made in 2016 for a previous year?

There is not a deduction for federal taxes paid for prior year federal tax liability.

There is a deduction for state and local taxes paid for prior year tax liability.

Take the following steps to enter these payments into TurboTax.

1. First, click on the Federal Taxes tab (or the Personal tab depending on version).
2. Click on Deductions and Credits and make sure to click on Jump to full list or Skip to All Tax Breaks if you don't see all deduction options.
3. Scroll down until you see the Estimates and Other Taxes Paid section and click Show More to expand the section.  
4. Click Start/Revisit next to Other Income Taxes Paid
5. Click Yes on the "About Other Taxes Paid" page.
6. Scroll down to Other Income Taxes Paid in 2016. (screenshot attached)
7. Click Start next to the appropriate section.