miniplug from the headphone jack on your minidisc player, and also miniplug on the other end of that cable to the audio input on your iMac.
Use Audacity to record your audio.
So, all you need is a simple miniplug to miniplug cable, in the length that you need.
In the event that the audio output from the minidisc player is too low, you'll need a USB to audio interface of some kind.
The iMic is still sold by Griffin Technology, and continues to be a good value - http://store.griffintechnology.com/imic
Or, you can try one of the other more-generic USB-audio sound interfaces. Some will work without any struggle on a Mac, despite often listing only Windows compatibility.
I've heard of folks using this interface with OS X: http://www.newegg.com/Product/Product.aspx?Item=N82E16812186035
but I have not tried it.
I would try the simple audio cable first, as that may work without any other hardware needed.