I'm assuming you are using Windows and have a CD burner (if not then more later)
You can simply run a cable from the headphone out or line-out of the MD player into the Sound-in on your soundcard and then you can record to a WAV file from your MD. There is various software out there that will handle the recording - at its most basic Windows Sound Recorder should do it, but if you can track down on of those "convert your old vinyl to CD" type packages (Steinberg Clean, Magix Deluxe Audio Cleaning Lab etc...) you will have more options for splitting tracks, and authoring your CDs. Other alternatives include Audacity (Free) and Cool Edit (which may or may not be free these days) Google will get 'em for you!
If on the other hand you have a Mac, the get a copy of Roxio's Toast which comes with CD Spin Doctor (and does much the same thing)
If your Sound card has a digital input (may be labelled SPDIF) the you should be able to do a digital copy, but I don't have any direct experience of that.
Hope this helps