Tagging in Azure is a massively useful feature.  I have customers who are interested in identifying resources for billing but they are also a very useful tool for control.  Resources can be grouped by tag and then a script can be used to apply a function to all machines or services with the same tag.

In the example below I call a variable that looks for Azure resources where the type is identified as a Microsoft virtual machine.  Calling this function enables me to extract a range of information. (I fact this script then goes on and uses the ResourceId too)

As referenced in Using tags to organize your Azure resources tags are updated as a whole so if you want to add additional tags you first have to call the existing tags.  In the example below I am adding the new tag to my existing tags.

Finally we are looping this for each vm and applying via a set command.

Hope this is of use to you, happy tagging :-)!

$FindVMs = Find-AzureRmResource | where {$_.ResourceType -like "Microsoft.Compute/virtualMachines"}
$Tags = (Get-AzureRmResource -ResourceId $ResourceId).Tags
$Tags += @{ Owner = "wade" }

Foreach ($vm in $Findvms)
{
$ResourceId = $VM.ResourceId
Set-AzureRmResource -Tag $Tags -ResourceId $ResourceId -Force
}

Disclaimer:  Please note although I work for Microsoft the information provided here does not represent an official Microsoft position and is provided as is.