// This will hold the urls
    private ObservableCollection<string> urls = new ObservableCollection<string>();

    private void Grid_Loaded(object sender, RoutedEventArgs e)
    {
        // Bind to our collection
        dataGrid.ItemsSource = urls;
    }

    private void button_Click(object sender, RoutedEventArgs e)
    {
        // Parse the url from our text and add it to our collection
        urls.Add(GetUrlFromText(textBox.Text));
    }

<DataGrid x:Name="dataGrid" HorizontalAlignment="Left" Margin="64,69,0,0"
            VerticalAlignment="Top" Height="152" Width="257"
            ItemsSource="{Binding}" AutoGenerateColumns="False">
    <DataGrid.Columns>
        <DataGridTextColumn x:Name="Urls" Header="Urls" Binding="{Binding Path=.}" />
    </DataGrid.Columns>
</DataGrid>