Jordan Zucker, an iOS expert at PubNub, demonstrates the simplicity of integrating PubNub into a new iOS project using CocoaPods, emphasizing its efficiency in managing dependencies for Swift and Objective-C Cocoa projects. CocoaPods significantly reduces the time required to add third-party libraries to an iOS project from 40 minutes to just 2-3 minutes, allowing developers to focus more on app development. The process involves creating an Xcode project, setting up a Podfile, running the 'pod install' command, and initializing the PubNub client with publish and subscribe keys, followed by setting up a basic publish-subscribe function using a test channel. This straightforward walkthrough highlights the ease of setting up PubNub with a simple message publishing feature, encouraging developers to explore the PubNub iOS SDK documentation for more comprehensive information.