When you make a page, you can select a template for the page ( in the right hand sidebar of the admin page where you edit the page ).
The templates are theme specific and you can find them as .php files in your theme directory.
Example from twentyten:
onecolumn-page.php. It starts with:
* Template Name: One column, no sidebar
* A custom page template without sidebar.
* The "Template Name:" bit above allows this to be selectable
* from a dropdown menu on the edit page screen.
Mark the * Template Name: One column, no sidebar line!!
Make a copy of a template you want to use for the page with the tag cloud, give it a different name and give it a different Template Name:
In this template, place the php code for the tagcloud. Then, create a page ( with no content ) and select your new template for it.