I have a new iphone 5 - I was organizing the apps into folders on the computer and after the sync the started shaking and won't stop...

Press the home button once

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DELETING APPS

Delete an App Store app: Touch and hold its icon on the Home screen until the icon starts to jiggle, then tap the “x”. You can’t delete built-in apps. When you finish, press the Home button.

Deleting an app also deletes all of its data. You can re-download any app you’ve purchased from the App Store, free of charge

Closing Apps

Double tap the home button then on the multitasking ribbon at the bottom of the screen hold one of the app icons until a minus sign appears and then tap the minus sign for all the apps you want to close. When done tap home button once.

Tap the screen somewhere once.

If that doesn tfix it then do this

Hold down the Sleep/Wake button and the home button together until the apple logo appears (ignore the ON/OFF slider) then let both buttons go and wait for phone to restart (no data will be lost).

to restart do what I said before

Here are the buttons

If you still can't figure out how to restart your phone then you need to read the manual at http://manuals.info.apple.com/en_US/iphone_user_guide.pdf

I am done. There comes a point where you really need to figure simple things out for yourself