How do I draw a shadow under a UIView?

A by far easier approach is to set some layer attributes of the view on initialization:

self.layer.masksToBounds = NO;
self.layer.shadowOffset = CGSizeMake(-15, 20);
self.layer.shadowRadius = 5;
self.layer.shadowOpacity = 0.5;

You need to import QuartzCore.

#import <QuartzCore/QuartzCore.h>