The penalty on early distributions from your Roth IRA account only applies to the earnings portion of the distribution. It does not apply to the amounts that you have contributed.

After you have entered your form 1099-R, TurboTax will take you back to the summary page titled Your 1099-R Entries.

On that page, click Continue and follow the TurboTax until you arrive at the page titled Enter Prior Year Roth IRA Contributions where you can enter the amount of your past contributions.

But the amount on that page (Enter Prior Year Roth IRA Contributions) seems to be asking me for the net of my contributions AND distributions.  I have withdrawn money from my Roth IRA...a lot.  In fact, my withdrawals exceed my contributions, which means I've benefitted from the earnings as well.  For example, if I had contributed $50,000 through the end of 2018 and withdrawn $58,000 during that same time period, I would have a negative number.  That's why I think I am going to have to put "0" in the blank and end up paying a hefty penalty.  Isn't that correct?

---

@talespinner wrote:

But the amount on that page (Enter Prior Year Roth IRA Contributions) seems to be asking me for the net of my contributions AND distributions.  I have withdrawn money from my Roth IRA...a lot.  In fact, my withdrawals exceed my contributions, which means I've benefitted from the earnings as well.  For example, if I had contributed $50,000 through the end of 2018 and withdrawn $58,000 during that same time period, I would have a negative number.  That's why I think I am going to have to put "0" in the blank and end up paying a hefty penalty.  Isn't that correct?

---

If that's your situation, then yes.  You can withdraw your original contributions any time without tax or penalty, but if you withdraw earnings, and it is not qualified (under age 59-1/2 or Roth open less than 5 years or both) then you owe regular income tax plus the 10% penalty. 

You would not enter a negative number, because presumably in some past year when you withdrew $58K on a $50K basis, you paid tax on that $8K.  Now, your number is just zero.  Just assume the question is asking "What is the amount of prior contributions remaining in the account before the withdrawal" (or more simply, "what is the after tax basis of your account").