To fetch data from a GraphQL API in React, first set up a new project with Next.js and install required libraries. Create environment variables for RapidAPI keys and load them into `next.config.js`. Sign up for a free account on RapidAPI and create an API key. Use the Now-CLI to develop locally by downloading the CLI and logging in to your ZEIT account. Fetch data from the Reddit GraphQL API using React hooks, including `useEffect` to run the API call when the component mounts. Display the fetched data in a user-friendly format with components for Subreddit, Twitter, and Giphy. The application uses one query and one API route, taking advantage of GraphQL's single endpoint concept.