The trick to sending content from your ipad 2 or or iPhone 4S or higher is to turn on mirroring. You double click and then slide backwards to click the airplay button - if you have no clue what I just said, you'll want to use this article from apple about how to do it.
App Advice is my favorite app for finding apps. This is their list of best apps for the Apple TV. The first one recommended is the REmote app. Just note that it is a bit tricky to learn to use the remote, but once you do, you may prefer it over the tiny apple remote that comes with the tv and keeps getting lost in the couch.
The read write web gives an overview of more airplay ready apps. An interesting note pointed out in this article is that instead of using the Apple TV remote, that one can use the netflix app instead and send movies to the Apple TV. The netflix ipad app is my favorite app for looking at Netflix - it gives recommendations that you can't get on the roku or Apple TV. Some other great ideas here as well.
You still have time to get an Apple TV if you have wifi and a pretty decent internet speed, it could make a great gift.
So, you don't understand why 2 screens are necessary and why the iphone/ ipad would need to be connected to a large TV. I have an Apple TV and beginning to use it with my ipad and the possibilities are revolutionary. I first heard of the Apple TV, most of the teachers who have 1:1 ipads in their school are using the Apple TV to wirelessly send content to their projectors.
This article from mashable thoroughly covers what the dual screen revolution means to the classroom and your family room.
"Dual-screen apps change all of that by shifting the software and user experience model from one user to potentially many, and from one screen (PC/phone/tablet) to two screens (phone/tablet and TV monitor). From a software development and user-experience perspective, the large monitor (which is the true second screen -- versus the standard concept that considers the tablet as the second screen) becomes an open computing surface where one can render any form of application functionality, information, data and content."
An excellent list of airplay enabled apps - although this was out a bit before the current Apple TV, I'm finding that these are some of the highest rated apps on the store with some very cool video capabilities.
For example, the free ShowMe app combs your networks and serves up video that your friends are watching -- not to your ipad (although that is possible) but to your TV that is enabled with the Apple TV. I'm finding the Apple TV higher quality than my Roku box, although I'm keeping my Roku box because it has Amazon and my Apple TV does not. If you get an Apple TV, make sure you set up Remote and download some of these apps.
Some great cases for the ipad. If you spend all this money at Christmas, make sure you get a good case to protect the ipad for your child. The thick rubberized cases like Otterbox are being purchased by many schools.
I am not sure why pinterest would confuse their brand by having Mikee Like as their button. My pinterest button literally changed to "Mike Like" it in Chrome and really, I'm not so happy about it. It is very similar to the pin button - this lets you pin to MikeLike, Pinterest, and Tumblr. I may reinstall pin from pinterest -- right click in Chrome and see if your pinterest button has been replaced. What a pain! The biggest issue is that MikeLike membership is by invite-only -- but this page can get you an invite. This is a drawback of add ins - if you put in an add in by a company other than the one who makes it, they can change it on you. I, personally, find this bothersome.