Unless you're willing to jailbreak your device or you're Steve Jobs, there's not a way to directly pipe your iPod touch, iPhone, or iPad's screen into a computer or projector. Teachers who use these devices with students would love to have this feature. Direct video from a handheld or slate allows for crisp, crystal-clear, and glare-free video of the the device. This could be projected on the wall so the whole class can see what's on the small device.
You might think that since Apple sells video cables and iPad VGA adapters that these would be good solutions for enlarging an Apple device's screen. Unfortunately, these adapters do not project everything you see on the screen--they are designed to only show photos and movies. In the case of iPad, apps must be programmed to output to the VGA adapter (and almost all are not), and the VGA adapter won't show the Home screen.
If you've got a document camera in your classroom, you're pretty good to go. Cameras from AVerMedia, Elmo, and Epson are popular, and they connect directly to a projector to show live video of what's under the lens. Unfortunately, document cameras can also be pricey. Some teachers have found less expensive USB web cams that do an acceptable job of showing a device's screen.
I've been on the hunt for a good portable USB camera. That's because I need it to travel with me, and the video needs to be directed through my computer so I don't have to switch video connections when toggling between my slideshow and the camera. In the past I've used an iSight Camera mounted on a flexible stand. Today the iSight is no longer available. I've recently been using using a Hue HD Webcam. I got it on sale for $30, but the problem is that the stand falls over when pointed down like a document camera.
Thanks to a suggestion I heard on the Bit by Bit podcast, I am now using the IPEVO Point 2 View USB Camera. It's $69 and gives a better picture than my cheaper Hue HD Webcam. Point 2 View is designed to be used like a document camera, so the base is weighted down. Point 2 View adjusts height and position using a multi-jointed stand instead of a flexible stand so it doesn't wobble.
Point 2 View comes with P2V software for Macintosh and Windows. This software lets you view the camera's feed in a window or you can go full screen. It also has a variety of adjustments if you want to try to improve the picture.
The camera has a one-touch focus button. I really like that it has two auto-focus modes. There's Continuous and Single. I keep mine on Single so that I can set it to focus on my iPod touch, and it doesn't change--even when my hand is in front of the iPod. Speaking of focus, this camera does a great job. Below is a screen capture to show you how clear the image is. Video from Point 2 View is better than other USB camera I've used.
When using a camera to show an iPod, iPhone, or iPad, I've found it looks best to turn the brightness setting on the device to about 20%. Be sure to turn off Auto-Brightness (in Settings app > Brightness) and adjust Auto-Lock (in Settings app > General) to 5 minutes or higher so the device doesn't keep dimming and turning off.
Of course, there are others uses in education for a USB camera like the IPEVO's Point 2 View. Check out IPEVO's Bring Your Curriculum to Life one-page PDF. Other resources for using document cameras include Teaching Tips from eMINTS and the Document Cameras in the Classroom handout.
Update May 13, 2011: After a year of using Point 2 View, the pin in the base has come loose and often falls out. I know others have also experienced this malfunction. Point 2 View's warranty is for one year, so the IPEVO will not replace my base. The company does not sell the base separately from the camera, so I have bought a whole new camera to replace the broken base. Though, I am not using Point 2 View nearly as much now that iPad 2 has video mirroring.