These functions will programmatically add widgets to a specified sidebar. This can be useful when a theme is first installed to fill specific sidebars with widgets you're written for your theme. $add_to_sidebar takes the id of the sidebar you wish to add to. $widgets takes the id's of the widgets you wish to add.

add-to-sidebar.php

<?php
function cur_add_widget_to_sidebar( $widget_name, $add_to_sidebar, &$sidebar_options ){

        $widget = get_option('widget_'.$widget_name);                                                                                                                                                       
        if(!is_array($widget))$widget = array();
        $count = count($widget)+1;
        $sidebar_options[$add_to_sidebar][] = $widget_name.'-'.$count;
        $widget[$count] = array();

        update_option('widget_'.$widget_name,$widget);
}

function cur_add_widgets_to_sidebar($add_to_sidebar = '', $widgets = array() ){

    $sidebar_options = get_option('sidebars_widgets');

    if(!isset($sidebar_options[$add_to_sidebar])){
        $sidebar_options[$add_to_sidebar] = array('_multiwidget'=>1);
    }   

    foreach( $widgets as $widget_name ) : 
        cur_add_widget_to_sidebar( $widget_name, $add_to_sidebar, $sidebar_options );
    endforeach; 

    update_option('sidebars_widgets',$sidebar_options);
}

functions.php

<?php

add_action('after_setup_theme', 'cur_setup_theme');

function cur_setup_theme(){
	if(!get_option('cur_widgets_installed',false)){

	        $add_to_sidebar = 'primary-navigation';
	        // $widgets is an array of widget id's
	        $widgets = array(
	            'search',
	        );
	        cur_add_widgets_to_sidebar( $add_to_sidebar, $widgets );
	
	        update_option('cur_widgets_installed',true);
	}
    }
}