Nothing is screwed up - you just need to close all the apps using the multi-task bar.
Double-tap the Home button and the top of the screen will slide upwards to reveal the multi-task bar at the bottom of the screen. There you'll see a row of icons that indicate the apps that are currently loaded. We need to close them all. Press and hold any one of the icons in the multi-task bar until they start to jiggle. Each icon will then have a 'X' symbol in its upper left hand corner. Press each 'X' and the corresponding apps will shut down completely. Do this for all the apps. Now touch the Home button and the multi-task bar will close.
Now you're back to the regular Home screen and you can try and open an app again. You should find that they will work OK this time.
Tim