Anywhere.FM you would like to download? The first you should do is to take note of the artist and song name before the site random playback switches to another tune. Then download a software called Orbit which will help you to catch the download link for songs in this and other sites.
As you may have already noted, Anywhere.FM has a limit on the number of times you can skip a tune by pressing the forward button in the player control. Than can be bypassed by just switching between a user's list of radios, so if you want to download a song by artist X and the user has created a playlist for that artist, you could eventually have your desired song playing again after switching back and forth between that and another of the user's playlists.
But before you do the switching and get to play your tune, you have to install Orbit and click on the Grab++ option in the Tools menu. That will open the link catcher that will get the download link for every song that the player hits. After that is just a simple download and renaming your saved file appropriately.
So, I recommend having Orbit's Grab++ window open whenever you listen to Anywhere.FM playlists. That way you'll save the time the switching takes, specially in populated playlists.