You need a hifi with a line out socket(usually marked Tape Record).
A cable from this to the line in on your Computers Soundcard (probably 2 phono to 3.5mm stereo jack ~£5 at most)
Set the record playing and using some software(there is freeware on Tucows, Audiograbber is excellent
http://www.tucows.com/preview/193549.html) record to WAV(Better quality but 10x bigger file sizes) if you want it on CD or MP3 for playback on your PC/iPod etc.
Job done. YOu can 'fiddle with it to remove clicks etc and cut it into individual tracks if you choose.
Ian