You can deploy Beam on Railway by following the necessary steps which include creating a GitHub OAuth application, deploying your app and updating the callback URL with the new domain URL. The required environment variables such as DATABASE_URL, NEXT_APP_URL, and GITHUB_ID are pre-configured for you. Once deployed, you need to update the Callback URL in your OAuth app and then clone the Beam repository and connect it to your Railway project using the Railway CLI. After that, you can use the Prisma command to update the database schema for your MySQL instance on Railway. Finally, after completing all the required steps, you can access and sign in to your Beam instance and use its features such as creating posts, liking them, commenting on them, and enabling image uploads using Cloudinary.