Cool Edit Pro would be the easiest to use, and most effective software package. The demo is free.
Depending on what outputs the audio player had, you'd most likely need a 3.5mm jack to jack cable (99.9% of line in sockets on computer soundcards are 3.5mm). The cable goes into the 'Line In' socket on your computers soundcard.
I'd probably recommend plugging the other end into the headphone socket of the audio player, unless there's a dedicated 'Line Out' on the player. Headphone sockets generally output at a decent line level.
Press record in Cool Edit and play on the audio player, and away you go.
