Using app templates is the fastest way to get started with Apex Designer. An app started from a template can have initial UIs, data and processes already set up and ready to go.
The CRM Sample app contains some basic business objects and relationships, with a few examples of UIs created with the dynamic components library.
The Vacation Request Sample app contains a simple Camunda process model along with a task list, and specific UIs for process tasks.
The Doc Site Sample app is a simple documentation wiki style app, using the Apex Documentation library.