Deploying Calendso, an open-source alternative to Calendly, on Railway involves setting up a PostgreSQL database and Google API credentials. To deploy the instance, add the GOOGLE_API_CREDENTIALS environment variable and create API credentials in the Google API console. This includes enabling the Google Calendar API, setting up scopes, adding test users, and creating OAuth client IDs. After deploying the instance to Railway, set up the database schema, create a new user, and start the server. Make minor adjustments to the NEXTAUTH_URL and Google API credentials before the instance is ready for production use. With these steps, a self-hosted Calendso instance can be fully functional, allowing users to create events and share links with others.