Azure VM’s when you keep them running can cost you a lot of money. So stopping your VM when it’s not in use is certainly a good idea. However you should be aware that there are 2 kinds of ‘stopped’ which are unfortunately not equal.
The first method to shutdown an Azure VM, when connecting for example through Remote Desktop, is to Shutdown the Operating System. In this scenario you go to the Power options within Windows and select Shutdown. This will stop the VM from running but will NOT deallocate hardware. So you will still be paying for the VM hardware allocation.
Note: On the Azure Portal, you’ll see that the VM status will be ‘Stopped’
The second method, and the better one, is to go into the Azure Portal and Stop the VM. This will not only shutdown the VM but also deallocated reserved resources. No further costs will be charged(with the exception of storage for your VM disks).
Note: On the Azure Portal, you’ll see that the VM status will be ‘Stopped(Deallocated)’
If you want you can automate this using Azure Automation and a runbook: https://docs.microsoft.com/en-us/azure/automation/automation-solution-vm-management