Exact procedure really depends on your environment and planned upgrade procedure but cloning the environment means that you create an 'exact' copy of your current environment first and run the upgrade on it after. So
theoretically to have the identical environment before starting the upgrade you would clone your AT to WS2003 and make sure that it works as expected with your cloned DT. Then already as part of the upgrade process you would reinstall the OS and would
have to go through the full AT installation and configuration again.
It may look like unnecessary step because reinstalling OS completely removes what you have installed on AT so you may think that you could just run directly new OS installation and TFS2012 with upgrade wizard but actually
there are a few things that may be different in TFS databases. I do not say that it is anything critical but if you want to be 100% super sure then you would probably go for cloning the old OS and TFS2010 first.
In both cases after new OS is installed you do not need to reinstall TFS2010 unless again you want to be 100% sure that everything works on the new OS (basically testing this way only OS upgrade) and this should be
done the way you plan to do it with your production. But again if not too paranoid you can
run directly TFS2012 installation and then Upgrade Wizard pointing to the Tfs_Configuration databases which will upgrade the data model.