Just start using an ST emulator on your PC. The best is STEEM and you can found it here: http://steem.atari.st/
Emulators use "disk images" instead of real disks. You put your atari disk in the pc drive and load it as a disk image. Then you can use it with STEEM. You can also copy any files you want to the "Hard Disk" which is just a folder on your pc hard disk. It's really simple.
For makind disk images try MAKEDISK. http://home.tu-clausthal.de/~ifmar/makedisk/index.pl?Site=Software
For better results, restart in MSDOS mode and run makedisk.