JSF does not include any persistency functions at all. It leaves that task for other frameworks, such as Hibernate.
To save a datatable after editing it, you need an action method that will be invoked when you click the "Submit" button on the form that displays the datatable. When that method is called, the dataModel that's backing the dataTable View will have been updated with the user's new values (after having first been validated). So at that point, it's up to you to provide logic to persist that dataModel out to the database.
When using an ORM such as hibernate/JPA, you can often use your Domain Model as the View Model, which can make the whole process fairly simple. Sometimes, however, the View model and domain models aren't quite identical, however, so in cases like that you'd have to build up and persist your own Domain Model.
If you're not using an ORM, and are, for example, using raw JDBC, you simply have to create code to iterate through the View Model and supply the appropriate JDBC insert/update functions.
An IDE is no substitute for an Intelligent Developer.