I decided the easiest way to airplay shows, and everything else, from my iPod Touch was to get an Apple TV.
My kids and I love ours! It is a little black flat square box that fits in my hand and connects to our wireless modem. Through it I can stream from my iTunes on my laptop, my iPod Touch, and the iPad2. In addition, we connect to our Netflix account through it! Searching through YouTube videos can be done straight through it also. We love watching TED Talks and Simon's Cat this way!
It offers many other things to connect to, but we don't spend a whole lot of time watching tv. We do enjoy the time we spend watching it though!
My little ones also love to watch game apps on the tv, which the Apple TV allows us to do! We will often read books together this way, and have been learning bits of other languages as a family using this! We love being able to airplay apps to the tv!
I hope this helps!