The answer depends a bit on whether these distributions are reported on a single Form 1099-R or on two separate Forms 1099-R. If they are reported on an single Form 1099-R, after you enter the Form 1099-R reporting the distribution from the traditional IRA TurboTax will ask what you did with the money. You'll indicate that you moved the money to another retirement account, that did a combination of rolling over, converting and cashing out, that you converted part to Roth (explicitly entering the amount), then you'll indicate that you put the money into an HSA (explicitly entering the amount of your HSA funding distribution). You'll also need to complete the HSA section to indicate your eligibility for the HSA contribution.
Form 1040 line 4a will show the entire amount of the distribution and line 4b will show only the taxable amount converted to Roth. Line 4b will also include the notation "HFD."
If the distributions are reported on separate Forms 1099-R (because the Roth conversion was done in-house so that the custodian knows to use code 2 for that portion but still needs to use code 1 for the HFD) the instructions are essentially the same except that you'll likely indicate that the entire amount of the one reporting the Roth conversion was converted to Roth and you'll indicate that the entire amount of the one for the HFD was cashed out and that you put the money into the HSA.
