This is probably one of the most blogged topics, so this post is mostly a helper for myself; to document how to access the different Online and Cloud services from Microsoft via PowerShell.
Windows Azure Active Directory is easy
$MsolCredential = Get-Credential
Connect-MsolService -Credential $MsolCredential
Windows Azure has multiple ways of doing it, but for quick access just
Add-AzureAccount
Exchange Online is a bit longer
# Set credentials
$UserCredential = Get-Credential
# Configure Session
$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://outlook.office365.com/powershell-liveid/ -Credential $UserCredential -Authentication Basic -AllowRedirection
# Import Session
Import-PSSession $Session
# Prefix trick when importing Session
Import-PSSession $Session -Prefix "EO"
# Turns for example Get-Mailbox into Get-EOMailbox. Could get handy
# Exit Session
Remove-PSSession $Session
SharePoint Online is no pain at all
Connect-SPOService -Url https://contoso-admin.sharepoint.com -credential admin@contoso.com
Lync Online is more like Exchange
$credential = Get-Credential
$session = New-CsOnlineSession -Credential $credential
Import-PSSession $session
Remove-PSSession $session