An Exchange Server 2010 Database Availability Group (DAG) needs a File Share Witness (FSW). This FSW is used to create a "majority" in case one of the servers fails. Although the DAG is fully managed from the Exchange Management Console or Exchange Management Shell, it still uses the Fail-over Clustering binaries under the hood. And the DAG is built on top of a Majority Node Set cluster.
But, for managing the DAG don't use the Fail-over Cluster Manager (under Administrative Tools). Use this only if you've run out of other options. The recommended way to manage the DAG is the Exchange Management Shell and the Exchange Management Console.
The FSW is just a server (a Hub Transport Server is recommended) with a fileshare that's used by the DAG members. If needed you can use a non-Exchange Server to serve as an FSW, but you have to add the Exchange Trusted Subsystem Universal Security Group to the local Administrators Group on the FSW Server. No additional software or service is installed on the FSW.
The FSW and the FSW directory are configured during creation of the DAG with the New-DatabaseAvailabilityGroup command, for example:
New-DatabaseAvailabilityGroup -Name DAG01 -WitnessServer CASHUB01 -WitnessDirectory C:\FSW_DAG01
You can check the DAG configuration using the Get-DatabaseAvailabilityGroup command, for example:
Get-DatabaseAvailabilityGroup -Identity DAG01 | fl
or if you only want to check the FSW option of the DAG:
Get-DatabaseAvailabilityGroup -Identity | Select Wi*
and accordingly, to change the FSW options of DAG01 you can use the Set-DatabaseAvailabilityGroup command, for example:
Set-DatabaseAvailabilityGroup -Identity DAG01 | Set-DatabaseAvailabilityGroup -WitnessServer CASHUB02