The Nexmo Client SDK allows developers to create chat applications with audio functionality, enabling real-time communication between users. To get started, install Node and NPM, set up a Vonage API account, and clone the demo application from GitHub. The script can be used to automate the setup process, but manual configuration is also possible. Once set up, the application allows users to log in, start chatting, and enable audio communication. The JavaScript code handles user events, such as sending messages and enabling/disabling audio, and logs errors using a custom error logger. With both users logged in and having enabled audio, they can hold a conversation between each other, with options to click on Disable Audio to turn the microphone back off.