iPhone, how does one overlay one image onto another to create a new image to save? (watermark)

It's pretty easy:

UIImage *backgroundImage = [UIImage imageNamed:@"image.png"];
UIImage *watermarkImage = [UIImage imageNamed:@"watermark.png"];

UIGraphicsBeginImageContext(backgroundImage.size);
[backgroundImage drawInRect:CGRectMake(0, 0, backgroundImage.size.width, backgroundImage.size.height)];
[watermarkImage drawInRect:CGRectMake(backgroundImage.size.width - watermarkImage.size.width, backgroundImage.size.height - watermarkImage.size.height, watermarkImage.size.width, watermarkImage.size.height)];
UIImage *result = UIGraphicsGetImageFromCurrentImageContext();
UIGraphicsEndImageContext();

If you want the background and watermark to be of the same size then use this code

...
[backgroundImage drawInRect:CGRectMake(0, 0, backgroundImage.size.width, backgroundImage.size.height)];
[watermarkImage drawInRect:CGRectMake(0, 0, backgroundImage.size.width, backgroundImage.size.height)];
...

The solution provided by omz also works in Swift, like so:

let backgroundImage = UIImage(named: "image.png")!
let watermarkImage = UIImage(named: "watermark.png")!

UIGraphicsBeginImageContextWithOptions(backgroundImage.size, false, 0.0)
backgroundImage.draw(in: CGRect(x: 0.0, y: 0.0, width: backgroundImage.size.width, height: backgroundImage.size.height))
watermarkImage.draw(in: CGRect(x: backgroundImage.size.width - watermarkImage.size.width, y: backgroundImage.size.height - watermarkImage.size.height, width: watermarkImage.size.width, height: watermarkImage.size.height))
let result = UIGraphicsGetImageFromCurrentImageContext()
UIGraphicsEndImageContext()

SWIFT 4

                    let backgroundImage = imageData!
                    let watermarkImage = #imageLiteral(resourceName: "jodi_url_icon")

                    UIGraphicsBeginImageContextWithOptions(backgroundImage.size, false, 0.0)
                    backgroundImage.draw(in: CGRect(x: 0.0, y: 0.0, width: backgroundImage.size.width, height: backgroundImage.size.height))
                    watermarkImage.draw(in: CGRect(x: 10, y: 10, width: watermarkImage.size.width, height: backgroundImage.size.height - 40))

                    let result = UIGraphicsGetImageFromCurrentImageContext()
                    UIGraphicsEndImageContext()
                    self.imgaeView.image = result

Use result to UIImageView, tested.