Another for Audacity
Agree with all the other Audacity fans, it's a great tool. I used it to transfer around 50 vinyls before consigning them to an overseas shipping company.
If you want to encode the results as MP3, you'll need the Lame encoder as well - MP3 is a proprietary format and so isn't included in Audacity by default. Lame is free too, by the way.
Audacity has the ability to detect track changes by looking for silence gaps but I found too many records with silence gaps within the tracks long enough to trigger the track switch! So I just record the entire side as a single file and break up the individual songs manually.
You will pick up all the "pops" and "clicks" from the original records and again, Audacity has a tool for clearing them automatically. But with a little practice, it's very easy, if more time consuming, to manually cut out the "pop" from the audio track (use zoom in to get a more precise waveform).
Do make sure you fill in the metadata when prompted by the export process exactly as the record sleeve, then, when you play your results with most of the media players, they will be able to find the right track detail from the Internet.
It's not the most user friendly program I've ever used but the learning curve it well worthwhile and you will learn a little about audio recordings along the way.