The two easiest options are:
1) Install the drive to a working computer and copy the files to its hard drive.
2) Install the drive into an enclosure, attach that to a working computer and copy the files to the working computer's hard drive.
No. First unplug the working computer (host) from the wall, open the side panel, find an empty hard drive bay, install the old drive, attach a data cable to the newly-installed hard drive and to an empty port connector on the motherboard, then attach the appropriate power cable to the hard drive.
Plug in the power cord, and power-on the system. When windows loads, you can use Windows Explorer to locate the old hard drive, select the folders and files you wish to copy, then paste them to a new location on the host computer's hard drive.