I'm having trouble wrapping my head around this and Google's sprawling documentation isn't helping (I can't even find a list of response types and their properties).

I have my storefront built in PHP and my shopping cart is stored in the session. When I hit the Google Checkout button, it posts to a different window (using the HTML API) and I get the Google sign-in where everything looks more or less right.

However, I don't know how I'm supposed to clear my shopping cart once somebody finishes an order. I haven't actually been through a test order because I can't get the sandbox directions to work (it keeps "forgetting" any settings). Does my callback page recieve any sort of message I should be handling? I'd like to do custom order processing someday but resetting the shopping cart is absolutely critical!