spiderling,
It's not that simple, the checkout success page is made up of dozens of different templates. You will need to figure out which template your code needs to be inserted in. Thankfully Qualiteam has made this easy.
Using webmaster mode you can easily discover what template you need to edit. I made you this video to explain this process. Sorry, it is a little slow, has no audio and is unedited.
http://www.youtube.com/watch?v=zqFaG1yvuFI
But I think it will get you on the right track to finding a specific template when you need it.
Hope this helps,
-Mike