I converted my father-in-law's vinyl to CD about a year and a half ago. I would start my PC recording and start the record playing and leave for about twenty minutes. Then I'd come back and start another recording, flip the record and leave for twenty minutes. This left me with two twenty minute long wav files which I would open up in a wave editor (I like Cool Edit Pro) and chop them up. You can usually tell visually where the breaks in songs are cos the heartbeat-looking graphical representation flatlines during the silence. Anyway, I'd just click and drag, highlighting the length of a song and then I'd choose an option, something like SAVE AS SEPARATE FILE and give it a track name.
This entire process was done for over 80 albums and we also printed CD labels and front and back CD jewel case covers for each album. It was a birthday present and his LP player was broken so he didn't even know that we had swiped his record collection even thouth it took us a couple months to get it all done. Turned out really damn cool. I'd never again
Cooledit will edit MP3's too so you can do it the way I did, and I remember seeing a piece of software some guy was selling that he had essentially made "in his garage" that would detect the splits in songs and cut them up for you, but it sounded pretty dodgy so I just did it all by hand.
It's pretty tedious....REALLY time consuming. You might be better served buying the album or looking for the songs online individually.