To add view animations to an iOS application using Swift 4 and Auto Layout, developers can use the Animation API provided by Apple. The animation process involves specifying the duration, delay, options, and animations closure for each property being animated. With these basics covered, animating appearance properties like color and alpha values is straightforward, while animating position and size requires more complex code to handle Auto Layout conflicts. By chaining animations using completion closures, developers can create more sophisticated animations that move views around the screen while changing their size and color. The end result is a beautifully animated view that responds to user interactions, showcasing the power of Swift 4 and Auto Layout in iOS development.