Often, audio is playing directly in your web browser, and not in a separate audio player. Getting Airfoil to transmit this audio is just a matter of selecting the proper source. In these cases, you need to select your browser as the source, as seen here:
Some examples of web-based audio for which you need to select your browser as the audio source include:
Just set your web browser as the source to easily capture audio from these sites, and any others, with Airfoil.