How would I go about doing somebody’s taxes that made me their power of attorney and they are in prison

If for 2023, you need to purchase turbotax to install on your computer, the online version will close soon.  If for 2024, you can use either the desktop or online.  

To actually file, you have 3 choices.

1. file online, as if you were the inmate, using their name and their tax info from last year and their drivers license to pass the verification to e-file.  I don't love this since it is not strictly according to the rules.

2. File by mail.  Prepare the return, print it out, and bring it to the inmate to sign.  No POA is needed.

3. Get the inmate to sign a form 2848, which is an IRS POA form, because of course they have their own form.

https://www.irs.gov/forms-pubs/about-form-2848

Or, use your own POA, but make sure it covers taxes.  Print the return.  You sign it, write "personal representative" next to it, and mail it to the IRS with either 

a. a fully filled out form 2848 signed by you and the inmate, or

b. a copy of form 2848 with your section signed by you, and attaching a copy of the POA signed by the inmate.

This is spelled out in the instructions for form 1040 under "signatures."

https://www.irs.gov/publications/p17