Styling php drop downs with CSS?

I’ve used the following code to add drop down menus for a client site:

<select name="archive-dropdown" onchange="document.location.href=this.options[this.selectedIndex].value;">
  <option value=""><?php echo esc_attr( __( 'Select Month' ) ); ?></option>
  <?php wp_get_archives( array( 'type' => 'monthly', 'format' => 'option', 'show_post_count' => 1 ) ); ?>
</select>

<?php wp_dropdown_categories( $args ); ?>

I’d love to style the drop downs – something like this: http://tympanus.net/Tutorials/CustomDropDownListStyling/ but can’t quite figure out how to make it work with the php. I tried wrapping the php codes in classes and div ids without much luck. Any ideas? When I search on styling drop downs, I seem to turn up a lot of tutorials about WordPress menus. It seems drop downs for categories and archives are a bit ‘behind the times’ but this client wants them, and I’d at least like to make them look nice for her.