Your situation and the way you handle it depends on from whom you inherited the IRA. If you inherited the IRA from a deceased spouse and you rolled the IRA into your own IRA, then the basis in that IRA is considered to be your basis now.
In that case for IRA accounts, the basis of all accounts is considered when you take a distribution from any of your IRAs. So, you do not specify a basis for each individual account, instead you report the total basis.
When you have entered all of your 1099-R forms reporting the distributions that you received in 2017, there will be some follow-up questions when you click Continue from the 1099-R summary screen.
One of those questions will ask if you made and tracked non-deductible contributions to your IRA accounts. Choose Yes and you will be able to enter the basis for your inherited IRA. There should be an EasyGuide option on that screen to take you through this process in greater detail if you like.
If the inherited IRA came from someone other than your spouse, then the basis of that account alone must be considered when determining the taxable amount of the distribution. TurboTax is not set up to be able to handle that calculation and it cannot track the basis for that account. You can still use TurboTax for your return, you will simply need to calculate the taxable amount of the distribution and keep track of the basis on your own.
TurboTax should handle this, I know other tax software does.
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TurboTax does not have the ability to track basis in an inherited IRA and does not have the ability to prepare the necessary Form 8606 to calculate the taxable amount of the distribution and to identify that Form 8606 as applying to the inherited IRA rather than the individual's own IRAs. The Form 8606 for the inherited IRA must be prepared manually and the taxable result entered into TurboTax when TurboTax asks for the amount of the distribution that is taxable. The manually prepared Form 8606 must then be included with your mailed tax return.