If you look in the Subscribe To Comments settings there are options about the header, sidebar and footer files to include as well as HTML to put before the subscription manager page and after.
Careful use of those options will cover just about any eventuality. Specifically, you need to use the before/after HTML to add any opening or closing DIVs that your theme takes for granted in files like index.php and single.php so that the page will work with your header and footer.
You can also add a custom CSS class around the whole page, then use that to target its contents with CSS.
It's pretty annoying that this stuff isn't mentioned in the plugin's Installation or FAQ sections, as I keep forgetting how I did it in the past and having to re-investigate.