A tutorial application which showcases the basic usage of a Vaadin CDI Application is available at https://github.com/vaadin/flow-cdi-tutorial. You can use this application example to test the different concepts and features presented in the documentation.
For starting a new project with CDI and Vaadin, you can get a project base for Vaadin and CDI from vaadin.com/hello-world-starters. It is a project template with the necessary configuration and dependencies included for starting building you own application. This starter is also available for cloning from Github.