You can complete form 8606 in the desktop version of TurboTax and that would allow you to determine your basis in an IRA. You would use the Forms option (on the menu bar) and search for form 8606.

when you enter your prior basis, and report a distribution

Form 8606 calculates your new basis. 

TurboTax supports Form 8606.

Does completing the Form 8606 automatically transfer the (1) basis and the (distribution) to the Form 1040?

If you enter your basis and value of your traditional IRA during the 1099-R section interview and trigger Form 8606 then TurboTax will automatically calculate the taxable amount and enters this on line 4b of Form 1040.

1. Click on "Search" on the top right and type “1099-R”
2. Click on “Jump to 1099-R”
3. Click "Continue" and enter the information from your 1099-R
4. On the "Your 1099-R Entries" screen click "continue"
5. Answer "yes" to "Any nondeductible Contribution to your IRA?"
6. Answer the questions about the basis and value

If you enter it directly into Forms then you will still need to  enter your 1099R on the 1099R Form. TurboTax will carry the information to Form 1040.