If it's any help, I run a small recording studio, and one of the services we offer is vinyl to digital transfers. I use a Garrard direct drive turntable and after LPs are evaluated for scratches/skips etcetera, I run the audio from the turntable to an analog preamp (I use a Neve 1073, a recording preamp used in many studios...typically you'll plug mics into them and from there to a recording console or direct to a digital audio workstation/computer) and from the preamp to my computer using a digital audio interface that converts the analog signal to digital and thereby into the software (I am using ProTools).
Good results can be achieved also by running the audio from the turntable outputs into the soundcard on your computer, assuming you have a soundcard that accepts the type of connectors you have on the turntable and you have software that can boost the signal level sufficiently and enable you to create MP3s or WAV files...
I'll gladly chat about it more if you have specific questions...
Good luck,
Jan-Mikael
www.erakare.com