Purchase and download the 2020 TurboTax software from this website - https://turbotax.intuit.com/personal-taxes/cd-download/
You don't need the CD. You can buy the program as a download from Turbo Tax or many stores like Costco. Even if you have the CD you can download it instead.
Buy the Download.....https://turbotax.intuit.com/personal-taxes/cd-download/
THEN to move your tax returns -
See this article on how to move your tax return to another computer…….
https://ttlc.intuit.com/community/tax-data-file/help/how-do-i-move-my-tax-data-file-to-another-computer/00/26128
What I would do is just copy the whole Turbo Tax folder that is under your Documents. That should be where the .tax files and pdf files are stored. Copy that folder to a flash drive or best yet is to burn it to a CD or DVD and then you will have a backup of them. Then on the new computer copy the folder (or files) from the flash drive to your Documents folder.
You only need the prior year .tax file to transfer into the current year. And actually you should open each year (if you still have the programs installed) and save each year as a pdf file if you haven't done that. Then you don't need the program installed to view your returns.