Hello. Very often Magento projects aren't plain and simple. Customization is so deep that you need to edit even Success Order page. I will give a try to put together all info about this page.
1. Success page - page you see when you press "Order Now" button on Checkout and your order is accepted.
2. checkout.xml - here you can change page layout and add CMS blocks
3. Template file is located:
app/design/frontend/yourpackage/yourtheme/template/checkout/success.phtml
4. Now you are ready to style it. But there is a problem. When you click "Refresh" on Success page you will be redirected to empty Cart page. Styling is nightmare in this conditions.
Solution: Temporarily disable clearing session. Find this file app/code/core/Mage/Checkout/controllers/OnepageController.php and comment line 227
// $session->clear();
5. Do all your styling magic according to designs, test for browser compatibility.
6. Important: Uncomment code you commented in step 4 because site will not work correct.
You are done! Show your result to the customer :)
Tested: Magento CE 1.6.0.x
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