I'm not sure quite where it would go in your own index.php at present, but let's assume you want to use the second example on the author's page.
The actual code you would use is something like:
<php if ( function_exists('show_featured_post') )
show_featured_post('', '', true, 42);?>
which he has helpfully explained means that you would always display a featured post from category 42, if the plugin was activated. This is what the if function exists part does.
It might help to look at some of the comments on that page as well, because it seems others were having some issues trying to get the plugin to work the way they wanted.