Using AirPlay from apps. It's supereasy to stream content from iTunes on your computer: Just click the AirPlay button () to choose the media's playback destination (that is, the Apple TV or AirPlay speaker you want to stream to).
Likewise, iOS apps often have the same AirPlay button to direct the media playback from iPads, iPhones, and iPod Touches. Some websites also display this button in their video players.
Tip: If you or your friends use Android devices, there's the free DoubleTwist Player Android app that can stream music and video via AirPlay via the $5 DoubleTwist AirPlay add-on. Just note that it works erratically.
The other thing you can do is use the free Remote app from Apple to have your iOS devices access content in the iTunes libraries on your computers, so they can listen to music, podcasts, or audiobooks; play iTunes U courses; or watch videos stored on those computers. That turns your iOS device into a portable TV or stereo. (The Remote app also lets an iOS device act as a remote control for the Apple TV, substituting for the remote control that comes with the Apple TV.)
To access the media on your computers' iTunes libraries, you need to set up Home Sharing on the Apple TV (via the Settings button), in your computers' iTunes (by choosing File > Home Sharing), and on your iOS devices (in the Settings app's Videos pane) so that they all have the same account. Doing so ensures the devices see each other.
Tip: Don't make your Home Sharing ID the same as your iTunes account. By keeping it separate, you can share the Home Sharing ID with family and friends who you don't want to be able to make purchases from your iTunes account.
Note: You don't need a Home Sharing account to stream content from an iOS device or from a Mac via AirPlay Mirroring; you need Home Sharing enabled only to stream content from your iTunes library. Anyone with a compatible device can stream to the Apple TV, a great party game if your friends are Apple users. (You can also set up a password for your Apple TV in its Settings app to prevent random streaming by visitors.)
You can share photos from computers and iOS devices via the Apple TV to your TV and to other iOS devices and Macs. The Photo Stream feature in iOS's Photos app and in OS X's iPhoto and Aperture apps makes it ridiculously easy to share photos with friends and family. If they have iCloud accounts, they can even comment on them -- great for remodeling projects, family vacation planning, and so on.
Using AirPlay mirroring. If an app or site doesn't have an AirPlay button, double-press the iOS device's Home button, swipe to the left in the multitasking dock that appears, then tap the AirPlay button when you see it to choose a playback destination and enable screen mirroring. Now, nearly anything you watch on your iOS device can be streamed to your TV. I say "nearly" because some iOS apps, such as NBC and Amazon Instant Video, block video streaming via mirroring as part of their DRM.
Note: Some iOS devices don't support AirPlay screen mirroring: the original iPad, the iPhone 4 and earlier smartphone models, and the fourth-generation (late 2011) and earlier models of the iPod Touch.
If you own a 2011 or later Mac running OS X Mountain Lion, you can also stream your Mac's screen to the Apple TV. That AirPlay Mirroring feature lets you stream content from sources other than iTunes to the Apple TV. For example, you can use it to watch videos from Amazon Instant Video, which Apple TV does not support.