To activate shuffle mode, go to the Now Playing screen. The Shuffle button is located to the right of the Fast Forward (>>) button and above the Chromecast button.
If shuffle is active, the icon will glow blue. You can just toggle it ON and OFF by tapping it.
Shuffle mode treats the play queue like a deck of cards. Each song will be randomized in the queue and played only once. The currently playing song will be placed at the start of the queue.