This KB will show you how to connect to Office 365 Exchange Online using PowerShell.
The requirements for this is Windows 7 SP1 and above or windows Server 2008 R2 and above.
Once done save code below as a .PS1 script:
$UserCredential = Get-Credential
$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://outlook.office365.com/powershell-liveid/ -Credential $UserCredential -Authentication Basic -AllowRedirection
Import-PSSession $Session