omprocess

I figured it out. Here is an example implementation which
includes registering sidebars ( kudos to Thematic which
contained the code that pointed me in the right direction).

<?php
if ( function_exists('register_sidebar') ) {
register_sidebar(array(
				'id' => 'right-sidebar',
				'description' => __( 'The primary sidebar'),
				'name' => 'Right Sidebar',
				'before_widget' => '<div class="widget-here">',
				'after_widget' => '</div>',
				'before_title' => '<h3 class="widget-title">',
				'after_title' => '</h3>',
));

register_sidebar(array(
				'id' => 'bottom-left-sidebar',
				'description' => __( 'The lower left sidebar'),
				'name' => 'Bottom Left Sidebar',
				'before_widget' => '',
				'after_widget' => '',
				'before_title' => '<h3 class="widget-title">',
				'after_title' => '</h3>',
));

register_sidebar(array(
				'id' => 'bottom-right-sidebar',
				'description' => __( 'The lower right sidebar'),
				'name' => 'Bottom Right Sidebar',
				'before_widget' => '',
				'after_widget' => '',
				'before_title' => '<h3 class="widget-title">',
				'after_title' => '</h3>',
));
}
?>

<?php
class wdwp1_google_search extends WP_Widget {
	function wdwp1_google_search() {
		$widget_ops = array('classname' => 'wdwpSearch','description' => __('Configurable Google Search Box'));
		$control_ops = array('width' => 300, 'height' => 350);
		$this->WP_Widget('wdwp_g_search', __('WDWP Google Search'), $widget_ops, $control_ops);
	}

	function form($instance) {
		$instance = wp_parse_args( (array) $instance, array( 'result_page' => 'search-results', 'g_pub_id' => 'partner-pub-partner-pub-xxxxxxxxxxxx:xxxxxxxxx' ));
		$result_page = $instance['result_page'];
		$g_pub_id = $instance['g_pub_id'];
		?>
        <label for="<?php echo $this->get_field_id('result_page'); ?>">
        Name of search result page:
        <input id="<?php echo $this->get_field_id('result_page'); ?>" type="text" name="<?php echo $this->get_field_name('result_page'); ?>" value="<?php echo esc_attr($result_page); ?>" />
		</label>
        <label for="<?php echo $this->get_field_id('g_pub_id'); ?>">
        Google Publisher Search ID:
        <input id="<?php echo $this->get_field_id('g_pub_id'); ?>" type="text" name="<?php echo $this->get_field_name('g_pub_id'); ?>" value="<?php echo esc_attr($g_pub_id); ?>" />
		</label>

        <?php
	}

	//function update($new_instance, $old_instance) {
		// processes widget options to be saved
	//}

	function widget($args, $instance) {
		extract( $args, EXTR_SKIP );
		$result_page = ( $instance['result_page'] ) ? $instance['result_page'] : 'search-results';
		$g_pub_id = ( $instance['g_pub_id'] ) ? $instance['g_pub_id'] : 'partner-pub-xxxxxxxxxxxx:xxxxxxxxx';
		?>
<div id="searchbox">
  <div class="inside">

<form action="<?php bloginfo('wpurl'); ?>/<?php echo esc_attr($result_page); ?>" id="cse-search-box">
<div>
<fieldset>
  <div>
    <input type="hidden" name="cx" value="<?php echo esc_attr($g_pub_id); ?>" />
    <input type="hidden" name="cof" value="FORID:11" />
    <input type="hidden" name="ie" value="ISO-8859-1" />
    <input type="text" class="searchfield" name="q" size="20" />
    <input type="submit" class="searchbutton" name="sa" value="Go" />
  </div>
</fieldset>
  </div>
</form>
<script type="text/javascript" src="http://www.google.com/cse/brand?form=cse-search-box&lang=en"></script>
  </div>
</div>
        <?php

	}

}

function wdwp_widgets_init() {
	register_widget('wdwp1_google_search');
	$default_widgets = array (
							 'right-sidebar' => array('wdwp_g_search-2')
							 );

    if ( isset( $_GET['activated'] ) ) {
    	wdwp_defaultwidgets();
  		update_option( 'sidebars_widgets', apply_filters('wdwp_default_widgets',$default_widgets ));
  	}
}

add_action('widgets_init', 'wdwp_widgets_init');

function wdwp_defaultwidgets() {
	do_action( 'wdwp_defaultwidgets' );
}

function wdwp_init_defaultwidgets() {
	update_option( 'wdwpSearch', array( 2 => array( 'result_page' => 'search-results', 'g_pub_id' => 'partner-pub-partner-pub-xxxxxxxxxxxx:xxxxxxxxx' ), '_multiwidget' => 1 ) );
}

add_action( 'wdwp_defaultwidgets', 'wdwp_init_defaultwidgets' );
?>