How do I Get a WPF DataGrid to Save Changes Back to the DataBase?

How do I get a WPF DataGrid to save changes back to the database?

I've data-bound my DataGrid control to a DataTable object, and populated that table with a very simple SELECT query that retrieves some basic information. The data shows up just fine in the control.

But when I use the control to edit the data, the changes are not pushed back to the DB.