Q: I have iOS device and Apple TV on the same network and both are running the latest software but can't see the airplay icon and am facing challenge with setting up the airplay mirroring

About AirPlay and Airplay Mirroring

AirPlay Mirroring requires a second-generation Apple TV or later, and is supported on the following Mac models: iMac (Mid 2011 or newer), Mac mini (Mid 2011 or newer), MacBook Air (Mid 2011 or newer), and MacBook Pro (Early 2011 or newer). For non-qualifying Macs you can try using Air Parrot.

Several Apple Articles Regarding AirPlay

Apple TV (2nd and 3rd gen)- How to use AirPlay Mirroring

How to set up and configure AirPort Express for AirPlay and iTunes

About AirPlay Mirroring in OS X Mountain Lion

iTunes 10- About playing music with AirPlay

Troubleshooting AirPlay and AirPlay Mirroring

Using AirPlay

Thanks to the $15 Beamer, AirPlay streaming is still possible on Macs  that do not support Airplay and mirroring.

Another solution is the Air Parrot.

What applications are you trying to mirror from? Not all apps support airplay

http://support.apple.com/kb/ht5209

http://support.apple.com/kb/ht4437

http://support.apple.com/kb/TS4215

 Cheers, Tom