ADO.NET is the core data access technology built into .NET that underpins nearly all libraries that provide access to relational data - be they ORMs (Even Entity Framework) or Typed DataSets or custom libraries you can find everywhere. If your goal is to access a relational database from .NET, there is little reason to not leverage ADO.NET at least for the low level API.
Both the other data access strategies discussed in the VistaDB documentation build on top of ADO.NET to provide a measure of convenience and reduce development cost and effort. That said, many applications choose to go direct to the ADO.NET API for data access and avoid the higher level abstractions the other data access methodologies provide.
VistaDB's core engine is an ADO.NET data provider. It fundamentally relies on ADO.NET to get it commands to execute, manage connections, and return results. Even when used from Entity Framework or another ORM in the middle is ADO.NET, exchanging commands and results.
This approach employs coding instead of a designer to create your data access layer. To get going, see Using VistaDB with ADO.NET - Getting Started for a step-by-step walkthrough of adding VistaDB to a project and performing basic database operations.
There are several sample applications that get installed with VistaDB 6. All of the samples are installed in the Public Documents folder on your computer, typically C:\Users\Public\Documents\VistaDB 6. Within the Samples folder look at the SimpleSamples collection to get started.