Google App Engine is a platform as a service that allows developers to easily deploy applications to the cloud. It offers both a standard and flexible environment. The standard environment provides preconfigured runtimes like Java, Python, and PHP, while the flexible environment allows customizing the runtime and operating system. Getting started involves installing the Google Cloud SDK, authenticating, and using commands like "gcloud app deploy" to upload code. Developers can then connect to services like Cloud SQL for databases and Cloud Storage for file storage. Google App Engine provides $300 in free credits for 12 months and always free usage tiers to make getting started cheap and easy.