Connect to Exchange Powershell website remotely (Office 365) and Exchange Server 2010, 2013

Start Powershell as a administrator

Run Windows PowerShell and check your Execution policy settings:

Get-ExecutionPolicy

If the execution policy is set to Restricted please change it to RemoteSigned or Unrestricted:

Set-ExecutionPolicy RemoteSigned

Provide the target server administrator credentials:

$LiveCred = Get-Credential

Configure the connection:
In the case of connecting to Exchange Server 2010, 2013:

$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://<target-server-address>/powershell/ -Credential $LiveCred

In the case of connecting to Exchange Online (Office 365):

$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://ps.outlook.com/powershell/ -Credential $LiveCred -Authentication Basic -AllowRedirection

Start the connection:

Import-PSSession $Session

To disconnect type in:

Remove-PSSession $Session