From the Lazy Admin. Cool dude Connect to Exchange Online with PowerShell - The Best Method (lazyadmin.nl)
1. Launch an elevated PowerShell window
2. Set-ExecutionPolicy -ExecutionPolicy RemoteSigned -Scope CurrentUser
a. Say Y
3. Install-Module -Name PowerShellGet -Force
a. Say Y
4. Install-Module -Name ExchangeOnlineManagement -Force
5. Update-Module -Name ExchangeOnlineManagement
6. Connect-ExchangeOnline -UserPrincipalName john@contoso.com
Now that you are connected you can run the next command to get the folder size information. Replace username with the user you want to look up.
7. Get-MailboxFolderStatistics username | Select Name,FolderSize,ItemsInFolder
When you finish, don't forget to disconnect
8. Disconnect-ExchangeOnline
