So by saying the plugin ‘works’, I meant that you can set the color for each category (from the admin panel where you add/edit categories), but that’s about it. There is no mechanism for being able to use those colors on your site.
The three lines of code I pasted above are PHP code that you put somewhere in your theme. You’ll need to edit the theme and paste them where you need them. Then you can use the contents of the $color variable somewhere in the HTML to do the styling. The colors are custom for each category and are not available in your CSS file, so you would use inline CSS on the tag you wish to style.
For example, if you are showing the category title at the top of each blog post, just under the post title, you may have the following code somewhere in your theme’s index.php:
<h2><?php echo single_term_title(); ?></h2>
You could use this plugin to have the category title be displayed in a custom color, like this:
<?php
$category_id = get_query_var('cat');
$colors = get_option('colored-categories');
if ($colors !== false)
$color = $colors[$category_id];
?>
<h2 style="color:<?php echo $color; ?>">
<?php echo single_term_title(); ?>
</h2>