The process for connecting PowerShell to your 365 (Exchange Online) tenant has been made a little easier. Assuming you are running a compatible PS version (and have previously set Set-ExecutionPolicy RemoteSigned) , on first run you need to run PS as admin and enter:
Install-Module -Name ExchangeOnlineManagement
Close and re-open PS and run:
Connect-ExchangeOnline -UserPrincipalName <UPN>
Once logged in, with MFA hopefully, you should be all set. Don’t forget to disconnect the session at the end:
Disconnect-ExchangeOnline
More details, including other options and switches, can be found here: