iOS 7 Solution:
You can display it in UIImageView and place on top of other UIViews. In the past, I used renderInContext in CALayer.
UIGraphicsBeginImageContext(self.view.bounds.size);
[self.view drawViewHierarchyInRect:self.view.bounds];
UIImage *blurImg = UIGraphicsGetImageFromCurrentImageContext();
UIGraphicsEndImageContext();
Once you capture UIView screenshot, apply blur effect. Unfortunately, there is no public API available yet for blur effect, but Apple has a sample implementation in sample code. It's a Category for UIImage. Please search a sample code in Xcode documentations. After adding UIImage category files to your project, you can blur an image like this:
blurImg = [blurImg applyDarkEffect];
Prior to iOS 7 Solution: https://github.com/tomsoft1/StackBluriOS
UIImage *blurImg = [originalImg stackBlur:radius];