My form 1099-R shows I paid both Federal and state income tax for an early retirement distribution? How/where do I enter these amounts to get credit for them?

Enter a 1099-R here:

Federal Taxes,
Wages & Income
(I'll choose what I work on - if that screen comes up)
Retirement Plans & Social Security,
IRA, 401(k), Pension Plan Withdrawals (1099-R).

OR  Use the "Tools" menu (if online version left side) and then "Search Topics" for "1099-R" which will take you to the same place.

Be sure to choose which spouse the 1099-R is for if this is a joint tax return.
Be sure to pick the correct 1099-R type: Standard 1099-R, CSA-1099-R, CSF-1099-R, RRB-1099-R.

[NOTE: When you get to the "Your 1099-R Entries" screen where you can add another 1099-R, use "continue" to keep going as there are additional interview questions after that screen in most cases. You can always return as shown above.]

All the information that's on your 1099-R gets entered on one screen. That screen includes boxes for federal tax withheld (box 4) and state tax withheld (box 12). TurboTax will put the amounts in the right place on your tax return.