Go to audacity.sourceforge.net, select your operating system and download and install Audacity onto your computer. This is a free, multitrack studio environment capable of recording and editing many types of audio files.
Open Audacity and go to "File -> Preferences." Select your sound card from the drop-down menu of recording devices.
Switch on your minidisc player and insert a minidisc. Connect the audio cable from the headphone jack on the minidisc player to the input on your computer. Note that if you have only a mono input, your recordings will not have any stereo effect.
Press "Record" on the minidisc player and "Record" in Audacity. Allow the recording to finish, then press "Stop" on both devices.
Go to "File -> Export" in Audacity, name the file and select the format you'd like to save it as. You can choose from WAV, WMA, MP3 and OGG, among others. Repeat Steps 4 and 5 for multiple recordings.