When I installed the style switcher, all I did was follow the instructions as it says word for word.
So just to be sure, ensure that:
You upload the wp-style-switcher.php file into your content/plugins/ dir
Enable the plugin in your admin panel
Change @import url( <?php echo $siteurl; ?>/wp-layout.css ); to @import url( <?php wp_stylesheet(); ?> ); in your index.php
You've already added the switch bit:
<?php wp_style_switcher(0); ?>
allowing to switch from the page.
It could be that your styles are not in the correct structure?
I would suggest wp-style/dir of style name/style.css so the css needs to be style.css not blue.css for example.
Go through the process again from scratch, it only takes a few minutes and I'm sure it will work.