So I turned on SSL in Hosting Service -> SSL Security Settings, the "Use SSL security in Shopping Cart" checkbox.
Now when I test checking out, my cart has no formatting. I suspect the problem is that the link to the CSS for the page layout in the checkout page is:
<link rel="stylesheet" type="text/css" href="http://www.triltech.net/shop/publish/slate.css">
And it probably needs to be https instead of http.
How do I fix this?