You can get an UIImage representation of the screenshot using something like this:
#import <QuartzCore/QuartzCore.h>
UIGraphicsBeginImageContext(view.window.bounds.size);
[view.window.layer renderInContext:UIGraphicsGetCurrentContext()];
UIImage *screenshot = UIGraphicsGetImageFromCurrentImageContext();
UIGraphicsEndImageContext();
Then you can do anything with it; maybe you want to write it to the Photo Library:
UIImageWriteToSavedPhotosAlbum(screenshot, nil, NULL, NULL);
As far as I'm concerned, immediate programmatical AirPrint printing is not implemented, you always have to go through the UIPrintInteractionController
class.