To simplify our approach, let's start with a basic source Exchange 2010 environment. A diagram showing the scope of the requirements is as follows:

Let's focus on the necessary requirements for the following components:
Directory Synchronization server
Active Directory Federation Services
Exchange Hybrid server
Only one Directory Synchronization server can be actively used within a single Office 365 subscription. The following are the base requirements for this server:
32-bit deployment—Windows Server 2003 SP2 or Windows Server 2008
64-bit deployment—Windows Server 2008 Standard or Windows Server 2008 R2
AD domain joined within the forest that you plan to synchronize with Office 365
Microsoft .NET Framework version 3.x installed
Windows PowerShell 1.0 installed
1.6 GHz+ processor
4 GB RAM (16 GB for 50 to 100 K objects and 32 GB for 100 K+ objects)
100 MB or 1 GB NIC
100 GB+ free disk space for an object count less than 100 K (if you plan...