What is the best way to record Internet radio?

I have found the free "Audacity" sound program to do this well. It has a "down button" on the upper right menu that allows you to change it to a number of settings, one of which is "What U Hear". That way you can start up the sound you are going to want to record, click on the Record button, and then Stop button when you're finished. On the webpage I'm showing below is also an add-on to this program called the "LAME mp3 encoder" which, when you install it, also allows the Audacity program to export the recorded sound file as an .mp3 to whatever folder you choose. That also is free. Good luck.