<data:DataGridTemplateColumn Header="Name">
        <data:DataGridTemplateColumn.CellTemplate>
            <DataTemplate>
                <TextBlock Text="{Binding Name}">
            </DataTemplate>
        </data:DataGridTemplateColumn.CellTemplate> 
        <data:DataGridTemplateColumn.CellEditingTemplate>
            <DataTemplate>
                <TextBox Text="{Binding Name}">
            </DataTemplate>
        </data:DataGridTemplateColumn.CellEditingTemplate> 
    </data:DataGridTemplateColumn>

It's clear example of Template column, right? What could be wrong with that? So, here is the thing - when a user navigates through DataGrid with hitting TAB-key, it needs to hit the TAB twice(!) to be able to edit text in TextBox. How could I make it editable as soon as the user gets the column focus, I mean even if he just starts typing?

Ok. I found a way - into Grid.KeyUp() I put the code below:

 if (Grid.CurrentColumn.Header.ToString() == "UserName")
        {
            if (e.Key != Key.Escape) 
            {
                Grid.BeginEdit();

                // Simply send another TAB press
                if (Keyboard.FocusedElement is Microsoft.Windows.Controls.DataGridCell)
                {
                    var keyEvt = new KeyEventArgs(Keyboard.PrimaryDevice, Keyboard.PrimaryDevice.ActiveSource, 0, Key.Tab) { RoutedEvent = Keyboard.KeyDownEvent };
                    InputManager.Current.ProcessInput(keyEvt);
                }
            }
        }