How to add animation while changing the hidden mode of a uiview?

Animate the view's opacity from 100% to 0%. Have the animation completion callback set the view to be hidden. You might also want to reset the opacity back to 100% during the callback, so the view will display fully opaque when you unhide it.

yourView.alpha = 0.0 //for zero opacity
yourView.alpha = 1.0 //for 100% opacity

There is no animation for hiding however; you get the same result with the Swift code below:

UIView.animate(withDuration: 0.2, delay: 0, options: [], animations: {            
    self.yourView.alpha = 0 // Here you can change the alpha property of the view 
}, completion: { _ in  
    self.yourView.isHidden = true // Here you hide it when animation done
})

Unfortunately, hidden is not a property that is animatable through UIView animations. I think your best bet may be to use one of the animations @Erik B suggested, or start dabbling with Core Animations which are much more powerful. Take a glance at the documentation for UIView animations and Core Animations.

I achieved something like what your suggesting by using UIView animations to slide the new view from below another view. This made it appear like a drawer sliding out. If you want to do something like that, you need to intercept the touch up inside event and place the animation code there.

- (IBAction)buttonClicked:(id)sender {
    [UIView animateWithDuration:0.5
                          delay:0.0 
                        options:UIViewAnimationCurveEaseOut
                     animations:^(void) {
                        self.myView.frame = /* set the frame here */
                     } 
                     completion:NULL];
}