If you guys are trying to get the search widget to look more like the “default style” search form (i.e. search button to the right of the input box on the same line), one way is to make a super tiny edit in the widget template file.
In the wp-includes folder, open widgets.php and look for the wp_widget_search function definition block (around line 405 or so). Within the definition block, look for this line:
<input type="text" name="s" id="s" size="15" /><br />
Remove the linebreak (<br />
), save, refresh your browser, and the submit button should now be to the right of the input box a-la the default theme.