Some people have already written that the AirPlay icon only appears when a compatible device is available -- this is true, but misleading. The AirPlay icon only appears when your iPad is connected to Wifi. So, start by going to your settings and making sure you are connected. Then double-click the home button and scroll to the far left to find your iPod controls and an AirPlay icon should appear if you have a new AppleTV on your network like I do. iPod music plays great.
Now launch Photos and use AirPlay to display a slideshow with music and...hey, what the?
Your AirPlay icon just vanished and your wifi connection on the iPad has terminated. Or maybe you got a few blips of music and one photo and then it froze.
Photos application and AirPlay don't like to play nice. You can see plenty of examples of this on YouTube already. The lag between actions on the iPad and synch to the AppleTV is confusing enough but sometimes just flicking between photos on the iPad is enough to dump the AppleTV back to the main menu. Music will cut in and out at the start of slideshows, sometimes flashing the covert art and description of the last song playing from the iPod and then flashing back to the music selected for slideshow. And sometimes it just gives up entirely and drops the wifi connection.
I suspect the AirPlay and the iOS multitasking teams never really figured out what would happen when AirPlay ran into conflicts -- two applications like iPod and Photos both trying to stream to a device at the same time. The error behavior isn't consistent and frankly the interface behavior isn't even designed to be consistent either. Slideshows only play on one device at a time but individual photos display in both places and thus can easily be out of synch. Want to display a Photo with AirPlay while picking out a song? Sorry, when you jump to iPod, your AppleTV drops the photo for its last menu. Sometimes the iPod shows itself playing but you get no sound. Slideshows run with no music when music is enabled.
AirPlay is simply a finicky, unreliable mess right now. Reboot your iPad and everything will probably work at least once. Hey, at least you don't need to use a paperclip to do it.