Deploying a Next.js application to production using Vercel, Sentry, and GitHub Actions involves bootstrapping the application, setting up Sentry for error tracking and performance monitoring, configuring Continuous Integration with GitHub Actions, deploying the application to Vercel, and testing the application in production. The process includes creating a new repository on GitHub, pushing the application to the remote repository, setting up a workflow file that triggers a linting step and a build step each time something is pushed to the main branch, and using Sentry Integration for Vercel to connect the Sentry project to the Vercel project in the Settings menu.