This information is lifted directly from the Joomla! Documentation
I put it here because I could never find it when I was looking for it. All rights to this code still exist with the original author.
There is actually a way of assigning a whole different template to a page not just a variation in the index.php file.
In Joomla! there is a default template, but you can assign other templates to specific "pages" that are defined by menu links.
To assign a template to a page, you must first make sure that there is a direct menu link to the page.
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Go to Extensions>>Template Manager
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Select the Template and click the edit icon (or click the template name)
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In the left column, change "None" to "Select from List."
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Select the links you want to apply the template to.
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Save
Note that you cannot assign the default template to individual pages.
Understanding
The templating system uses the ItemID to determine which template to show. ItemIDs are created when you create a menu link. This is why only menu items are shown in the list of pages to which you can assign templates.