For whatever reason, recording the audio streaming through your computer—whether that's an internet radio station, video game music, or an online presentation—is always a pain to do. Digital Inspiration shows off a way to do it easily with Audacity and a couple cables.
Depending on your particular setup, what you'll need to do here differs. If you're on a Mac, you can just set up Soundflower software so you're recording your system's audio. On some Windows PCs, you can just use the "Stereo Mix" setting. If you're on a computer that doesn't support either of those options (typically older Macs and lower-end PCs), you can use Digital Inspiration's hardware solution that essentially runs your computer's audio output right back into the input. The nice thing about the hardware solution is that you don't have to futz about with audio settings and additional software. Either way, once it's set up, you can record that audio easily in a program like Audacity. Head over to Digital Inspiration for the full guide.