What are the steps to perform to migrate from Office365 to an On-Premises installation?
I am aware that I can just copy/paste emails - but that is not a quite good solution for end customers.
My setup is running Exchange 2010 SP2.
The simplest and most supported option would be to setup an on-site Exchange box and then setup coexistence between Office 365 and your on-premise box and then simply migrate users from the cloud mailboxes back down to your on-premise box. Once everyone is migrated simply kill the coexistence.
Essentially reverse MSFT's instructions for setting up coexistence a bit.
This is probably the easiest AND still supported by MSFT if you have issues since it falls under the premise of coexistence.