All you will have to do is to scan your receipt and upload it on this page, it will be updated with instructions after the release:
http://www.apple.com/osx/uptodate/
After 3-4 days you will receive a password protected PDF email from Apple with your app code which you can redeem on the App Store to install ML.
It works much easier than that.
Once it is released. You enter your Serial into the Mac Up To Date Page: http://www.apple.com/osx/uptodate/
They validate your Serial Number was purchased during this window, and they email you a code you can redeem in the App Store. When you redeem the code it is associated to your iTunes account and can be downloaded on any Mac it is compatible with.
The code is generated instantly. I did this with my current MBP going to Lion. Too about 2 minutes to do.
The problem was that some of our serial numbers didn't work, we then had to contact AppleCare or scan our receipts. For most people (except me) it was smooth.