While there's no official extension available for Google Music beta, you can however, install a third-party Chrome extension called "Better Music Beta," that when installed adds a button that shows information about the currently playing song, lets you pause the song, go to the next song, add a thumbs up or a thumbs down. There's also a notification that shows up every time the song changes.
Another interesting thing is that, even though Google Music lists Flash as a requirement, the service works pretty well on an iPad.
To use Google Music on your iPhone or iPad, just visit music.google.com from your mobile browser and then choose the music you want to play. You can use the built-in controls with a double tap of the home button or the music bar at the bottom of the app.
Google Music is harder to use on the iPhone, sometimes requiring multiple taps to start playing, but your experience may vary and it won't scroll correctly for some users.
If you face any problem while playing Google Music on your iOS devices, here's a trick to make Google Music work every time: "start playing a song, pause and play again." It's because Google Music doesn't support iOS Safari. The supported browser includes: Chrome, Firefox, Safari, and Internet Explorer 7 and above" and that you need Adobe Flash.
It's interesting that this trick lets you play music on more than one device simultaneously.
Here's the video demonstrating Google Music on iPad and iPhone: