In order to add media to an exhibit Site, an Item Set will need to be added in the Resources tab of the site. Once the Item Set is added to the Site, all of the items will be grouped together and available to add to a page.
This screenshot shows the "Ski Archive" Item Set is added to the "Ski and Snowboard Archives" exhibit site. Once this is done, items from Ski Archive Item Set can be added to the pages within the exhibit.