One more easy way carries forward from the external-USB approach but is a bit cheaper (and probably temporary) in that it doesn't depend on an enclosure. Rather it simply uses an inexpensive SATA/IDE-to-USB adapter.
You just remove the old drive from its internal mounting, connect a few cables (power and data) to the adapter kit, sit the drive on the cardboard carton the adapter came in as a "temporary home", and plug in the USB end of that cable to a USB port on the computer.
I've used
this $15 kit purchased at Micro Center on two old machines which family/friends were upgrading to new boxes. We had no intention of retaining the old drive, so this temporary non-enclosure approach was fine.
Obviously, this is merely the physical solution to how you make the old drive available to the new machine or new Windows installation. Dealing with or protecting yourself from the potentially virus-infected files on the old drive is another matter entirely.
NOTE: as with any USB/removable device, if you want to disconnect the drive from the PC you should first "safely remove hardware", to let Windows flush out any data buffers and disconnect from the drive. When you get "it is now safe to remove..." message then you can pull the USB cable out from the PC. Then you can pull the power cord from the wall.
I repeat: do NOT pull the power cord from the wall first (while Windows still has communication to the USB drive and a drive letter is still allocated). Only pull the power cord out once you have done the "safely remove hardware" action and it's completed, and Windows has de-allocated the drive letter, and you've now pulled the USB cable out of the computer.