In theory it is simple!
Connect output from the turntable to the line input on the sound card.... using the soundcard's software record as a .wav file.
Snags.... The output from a modern turntable is insufficient unless fed through a pre-amplifier.
You may have to use your old amplifier and cut the volume to a minimum to avoid gross distortion.
You may not have any suitable software... I use Audacity which is a freebie download, this has a reasonable amount of editing facilities ideal for cutting out the cracks and pops of scratched vinyl.