If you go to Marketing > Nav Menu Promotions, you can add a variety of additional promotional items to your navigation menu, including a link to a Volusion-supplied ASP file that will accept hard-copy mailing information and add them to your customer table, specifically marking the Catalog Subscriber field as shown in the Optional Fields section of the customer account page.
When a shopper clicks the Request button, they'll go to a new page where they can enter all their address information.
When you're ready to send out new catalogs, you can export the relevant fields from the customer records to a CSV file so that you can generate mailing labels — you could generate your own saved query to only export those records which have the CatalogSubscriber field set.
Sample code (which assumes a non-white background in the navigation menu) that you can use as a template is as follows:
<form name="MailingList" method="post" action="/Catalog_subscribe.asp">
<span style="font-weight: bold; color: white">Want a printed catalog?</span><br>
<input type="submit" name="Submit" value="Request Catalog">