Make sure you're running WordPress version 2.3 or better. It won't work with older versions. Really.
Download the zip file and extract the contents.
Upload the 'wp-cumulus' folder to your plugins directory (wp-content/plugins/).
Activate the plugin through the 'plugins' page in WP.
See 'Options->WP Cumulus' to adjust things like display size, etc...
In order to actually display the tag cloud, you have three options.
Create a page or post and type [WP-CUMULUS] anywhere in the content. This 'tag' will be replaced by the flash movie when viewing the page.
Add the following code anywhere in your theme to display the cloud. <?php wp_cumulus_insert(); ?> This can be used to add WP Cumulus to your sidebar, although it may not actually be wide enough in many cases to keep the tags readable.
The plugin adds a widget, so you can place it on your sidebar through 'Design'->'Widgets'. The widget uses a separate set of settings, so it's possible to have different background colors, sizes, etc.