To organize Animal Crossing players using Twilio Programmable SMS and Flask, developers need to create a Python program that receives message notifications from Twilio, parses phone numbers, and updates a dictionary with player statuses. The program uses Flask to receive webhook requests, Twilio's API to send messages, and ngrok to expose the Flask application to the public internet. Users can add themselves to the directory by texting their Twilio number with "hello," change their status by sending specific messages, and check their status by sending "check." The program also includes features like message restrictions and help text for users who need assistance. With this app, friends can organize and socialize in Animal Crossing while maintaining social distancing.