To connect to Office 365 Exchange Management Shell, use the following method (this uses modern authentication and works with or without Multi Factor Authentication – MFA):

1. Run Windows Power Shell as Administrator
2. This step only needs to be done once on each PC you are connecting from:
   • Run: Install-Module -Name ExchangeOnlineManagement -RequiredVersion 2.0.5
     For an updated command and new versions check PowerShell Gallery.
   • Run: Import-Module ExchangeOnlineManagement
3. Run: Connect-ExchangeOnline
4. Log in with your Office 365 admin credentials.
   
5. To test a successful connection, run: Get-Mailbox
6. To disconnect, run: Disconnect-ExchangeOnline

==============================================================================
====================== Old Method (Basic Authentication, no MFA) ======================
==============================================================================

Following instructions will help to connect Windows PowerShell to your Microsoft Exchange Online or Office 365 service.

1. Run Windows Power Shell as Administrator
2. Run Set-ExecutionPolicy Unrestricted
3. Run $LiveCred = Get-Credential
4. Provide your Office 365 administrator account credentials
5. Run $Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://ps.outlook.com/powershell/ -Credential $LiveCred -Authentication Basic -AllowRedirection
6. Run Import-PSSession $Session

You should now be connected to your Office 365 account. To test connection you can run Get-Mailbox which should list all mailboxes in your Hosted Exchange account.

To disconnect from the service run: Remove-PSSession $Session