How do I include a third party designee on my taxes, so that they are allowed to discuss matters with the IRS?

That is not possible using the TurboTax online editions.

If you are using the TurboTax desktop editions, click on Forms.

When in Forms mode on the Federal Information Worksheet (Info Wks) scroll down to Part VI Additional Information for Your Federal Return.

Complete the Third Party Designee section

I suppose if you are using the Online version you can print it out and write it in.  But then you would have to mail it.

You would prepare a Form 2848 and send it to the IRS.

This is the form for a Power of Attorney and Declaration of Representative