To use WhatsApp Reply Context with Content API and Twilio Sync, developers need to set up their environment by creating a new directory, initializing it with `yarn init`, installing required modules, and setting up environment variables. They then create content using the Twilio Content Editor, copying the Template SID, and filling in the environment variables. Next, they write code to send a sample message registering the context within Twilio Sync, and add a function to register the message using Twilio Sync. The function takes the original replied message as an input and processes it by fetching the corresponding context from Twilio Sync. If no context is found, it sends a default message; otherwise, it sends a personalized response based on the button payload. To deploy this functionality, developers can use the Twilio Serverless Toolkit to create a Twilio Function that runs on every incoming message with a quick reply option. This allows businesses to understand which message their customer is replying to and take different actions accordingly.