How to add/save/retrieve additional fields to all available widgets?

Question

I cant seem to find any complete tutorial that shows how to add / save/ retrieve a fields to any widget. Can someone please show a simple example how to add a simple select , save the data and retrieve it in front.

All I got so far is this http://prntscr.com/76d051

add_action('in_widget_form', 'add_widget_fields');
function add_widget_fields(){


    $html ='<select class="custom_widget_select" name="dont know">';
    $html .='<option value="blue">Blue</option>';
    $html .='<option value="red">Red</option>';
    $html .='<option value="green">Green</option>';
    $html .='</select>';

    echo $html;

}

I dont know what name to use , how to retrieve it once is saved and how to display it in front for all widgets.

I just need to add simple select to display list of additional widget styles. and I would like to do this trough theme functions.php rather than creating a full blown plugin.

Any help is appreciated.