Hello jperry, welcome.
If you don`t have a "Line In" socket then you`ll have to use the "Microphone" jack.
The only problem I can see is the volume level.
Does your Minidisc player have "Line Out" as well as "Headphone" jack? If so, you`re halfway there.
"Line Out" has a nominal level of 1Volt peak-to-peak. Your Mic input requires only millivolts so you`ll have to reduce the output level of the Minidisc... either with the remote control or in the Menu.
If your Minidisc only has Headphone Out then you`ll just have to reduce the output even further.
Do you have any recording software installed on your PC?
If you have CD/DVD burning software you may find that it also has an audio recording facility. Also your sound card may have software for recording.
If you can`t find anything on your PC with which to record from your Minidisc then check out the "Downloads" section on the left of this screen.
If this doesn`t cover it please ask more, preferably with some more specific info regarding your kit
Good luck, let us know how you get on.