Get your taxes done using TurboTax

I was assuming you didn't have any non-deductible traditional IRA money to begin with, but the program does ask you about that so it should still work in that case. You do need to have sufficient earned income to do the non-deductible IRA contribution.

You do enter the non-deductible contribution in the section where you enter IRA contributions as you mention. When you enter the 1099-R form you do answer the questions regarding IRA balances. 

Line 8 on form 8606 does list the conversion amount and the lines below it are used to determine the taxable amount listed on line 15.