I am trying to use Windows Azure PowerShell to copy a zip file into VM. I have managed to connect to VM following the documentation.
But, I cannot find any tutorial
You cannot use PowerShell to copy a file directly to a Virtual Machine's OS disk (or even to one of its attached disks). There's no API for communicating directly with a Virtual Machine's innards (you'd need to create your own custom service for that.
You can use PowerShell to upload a file to a Blob, with Set-AzureStorageBlobContent.
At that point, you could notify your running app (possibly with a Queue message?) on your Virtual Machine that there's a file waiting for it to process. And the processing could be as simple as copying the file down to the VM's local disk.