You can use SQLite in WPF the same way you would use SQL Server, Oracle or any other database -- via ADO.NET or (better) via an object-relational mapper. An ORM is probably a better option because a good ORM will handle things like property change notifications (critical for data binding) for you.
The basic technique you are looking for is to define a model which you will load and save via the ORM, and databind your UI to using data binding. (The full version of this pattern is called model-view-viewmodel or MVVM but as a beginner you probably want to focus on the basics of creating and binding to a domain model first and tackle the more complex aspects of MVVM later.)
For more on SQLite visit http://sqlite.phxsoftware.com/