Download a live stream recorder, being sure to follow the individual instructions for the program you choose. Live stream recorders include Replay Music, Freecorder 4, and Wondershare Streaming Audio Recorder; not all are free.
Open your chosen live stream recorder and check the settings. Be sure your output format is MP3, and that your output directory is set to where you want the new music to be sent (for example, on a PC: C\Windows\MyMusic).
Open Napster and select the streaming audio function. Go to your live stream recorder and make sure it recognizes that Napster is playing. When it does, hit "Record." You can record multiple songs without stopping between each, as the recorder will recognize each individual MP3 file.
Press "Stop" or "Record" again (depending on your recorder) to stop recording. If your recorder doesn't automatically save your files, be sure to save them yourself.