How to set the DataSource of a DataGrid in WPF?

You can use the ItemsSource property :

<ListView ItemsSource="{Binding YourData}">
    <ListView.View>
        <GridView>
            <!-- The columns here -->
        </GridView>
    </ListView.View>
</ListView>

If you prefer to use code-behind rather than a binding, just give a name to the ListView and set the ItemsSource property in code:

listView1.ItemsSource = YourData;

You can also use the ItemsSource property with other list controls (DataGrid, ListBox, ComboBox, etc), since it is defined in the ItemsControl base class.

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EDIT: if the data source is a DataTable, you can't assign it directly to ItemsSource because it doesn't implement IEnumerable, but you can do it through a binding:

listView1.SetBinding(ItemsControl.ItemsSourceProperty, new Binding { Source = YourData });

This is simple an example:

XAML part :

<DataGrid Name="dataGrid1" Width="866" Height="auto" HorizontalAlignment="Left" VerticalAlignment="Top" />

C# part :

... [code to read and fill your table ] ...

da.Fill(myDataTable);
dataGrid1.ItemsSource = myDataTable.DefaultView;

And now your DataGrid will be filled with your DataTable

The GridView is a view and not a standalone control as far as i know, you would normally use it as the view of a ListView. In WPF the property for data population is called ItemsSource, you probably want to either use a ListView or DataGrid to display your data that way.