When you hear a song on the radio, or during a TV show, movie, or anywhere else, using the Google Sound Search widget is a quick way to identify it. Just tap the widget and it will start listening to the music. Once identified, you can find out more information.
The Sound Search widget also keeps a convenient history list of any tracks you've identified. To access it, just tap icon on the widget.
With the current Web version of Google Play Music, you would need to look up each track and add it to a playlist, since there's no interface option to display your sound search history. Fortunately, by visiting this link you can listen to the songs that were identified with the widget. You will likely need Google Music All Access to hear most of the music.
An image posted on the Google Europe blog shows Sound Search as a menu option in Google Music.