How to Bind Button to DataGrid Delete Command in WPF

I'd like to delete rows from a WPF DataGrid by clicking a button above (not inside) the DataGrid, following the MVVM pattern. Although delete buttons within a row itself work, they are kind of ugly (one has to select the row first) and as there are also add and edit buttons next to the delete button, a delete button would better fit there, I think. The corresponding part in my ViewModel looks like this:

<Button Grid.Row="0" Grid.Column="0" Content="add"/>
<Button Grid.Row="0" Grid.Column="1" Content="edit"/>
<Button Grid.Row="0" Grid.Column="2" Content="delete"/>
<DataGrid Grid.Row="1" Grid.Column="0" Grid.ColumnSpan="3" 
    ItemsSource="{Binding dataTableListItems}">
    <DataGrid.Columns>
        <DataGridTextColumn Header="Name"/>
        <!--I don't wan't to use these "in-Row" delete buttons-->
        <DataGridTemplateColumn Header="delete">
            <DataGridTemplateColumn.CellTemplate>
                <DataTemplate>
                    <Button Command="Delete" Content="X"/>
                </DataTemplate>
            </DataGridTemplateColumn.CellTemplate>
        </DataGridTemplateColumn>
    </DataGrid.Columns>
</DataGrid>

Any ideas on how Command Binding for the buttons could look like? Or alternatively, I could also be satisfied if the in-row delete buttons would always be enabled and a click on one would delete the corresponding row without needing to select the row first.

Assuming you're using MVVM, just bind to the SelectedItem of the DataGrid and use it whenever the Command is invoked.

Example ViewModel:

public class MyViewModel : INotifyPropertyChanged
{
    private Item _selectedItem;
    public Item SelectedItem 
    {
        get { return _selectedItem; }
        set
        {
            _selectedItem = value;
            RaisePropertyChanged("SelectedItem");
        }
    }

    private ObservableCollection<Item> _dataTableListItems;
    public ObservableCollection<Item> DataTableListItems 
    {
        get { return _dataTableListItems; }
        set
        {
            _dataTableListItems = value;
            RaisePropertyChanged("DataTableListItems")
        }  
    }


    public ICommand DeleteCommand { get; set; }

    public MyViewModel()
    {
        DeleteCommand = new RelayCommand(DeleteSelected);
    }

    private void DeleteSelected()
    {
        if (null != SelectedItem)
        {
            DataTableListItems.Remove(SelectedItem);
        }
    }
}

Updated XAML:

<Button Grid.Row="0" Grid.Column="0" Content="add"/>
<Button Grid.Row="0" Grid.Column="1" Content="edit"/>
<Button Grid.Row="0" Grid.Column="2" Content="delete" Command="{Binding DeleteCommand}"/>
<DataGrid Grid.Row="1" Grid.Column="0" Grid.ColumnSpan="3" 
    ItemsSource="{Binding dataTableListItems}"
    SelectedItem="{Binding SelectedItem}">
    <DataGrid.Columns>
        <DataGridTextColumn Header="Name"/>
        <!--I don't wan't to use these "in-Row" delete buttons-->
        <DataGridTemplateColumn Header="delete">
            <DataGridTemplateColumn.CellTemplate>
                <DataTemplate>
                    <Button Command="Delete" Content="X"/>
                </DataTemplate>
            </DataGridTemplateColumn.CellTemplate>
        </DataGridTemplateColumn>
    </DataGrid.Columns>
</DataGrid>