You asked: "How do I download tax processing software ?The site looks like it keeps all my data separate from my computer.??"
You didn't mention a tax year, so I'll assume you are asking in regard to preparing a 2020 return.
Are you currently using Online TurboTax (web version?) If so, in that online product one uses a browser to work on the return, and the data is stored online, not locally on your computer. It is the desktop software (CD/download), that one can install on one's computer and not have to use Online TurboTax. In the desktop products the data files are stored locally on one's computer. So are you asking how to purchase a download of the desktop software to install on your computer?
We don't know what you have already done or not. Have you already purchased the desktop software and just need to download it? Or are you asking where to buy it? If you haven't bought it yet and want to buy it directly from TurboTax, here is the page for 2020 tax product:
If you need prior-year software (2019, 2018, 2017), here is where to buy
If you already started a 2020 return in Online TurboTax and want to switch to 2020 desktop software, see this FAQ on how to download your *.tax2020 data file and continue it in the desktop product without having to start over.
FAQ: How do I switch from TurboTax Online to the TurboTax software?
From Online version,
you can download a Turbotax file with your return in it.
The file is useless unless you install the TurboTax software for that year together with the state program(s) for state returns attached therein.
Meanwhile, Print a PDF of your return for your records and keep it in a safe file cabinet.
FYI - if you want to buy the Turbo Tax Desktop program either on CD or buy the download.
Window System Requirements
Mac System Requirements
How to install on Mac
How to install Turbo Tax on Windows