If your processor is not an already integrated solution with ShopSite, then your options are limited. If you have ShopSite Pro, you could write an order API script that passes the data to your provider's system, or use the Javascript on the thank you page to do so.
http://www.shopsite.com/help/8.1/en-US/ ... r.api.html
http://www.shopsite.com/help/8.1/en-US/ ... ables.html
If it's just a page where they go and make a payment, you could give them a link to it, but then none of the details of the order would be passed along like the total, etc...