Install a sound card with an optical input, like a Creative Labs, on your computer, then run an optical TOSLINK cable from the player to the optical input of your computer.
Open Audacity, and choose the sound card input in Audacity, then hit pause/record.
Insert a CD into your player and hit play on the player, and record on Audacity. Audacity will record the optical output as a .wav file. Record each song you want from the original disk as a separate file.
Install the LAME .MP3 encoder into Audacity if you haven't already done so.
In Audacity, click Export and choose MP3 as an option. Choose your MP3 bitrate, up to 320kbps, and save the recorded .wav file as an MP3.