Access to Azure Portal
Locate the cloud service (classic) under http://portal.azure.com that hosts the virtual machine(s)
Add a user to to the service using their Microsoft account. For the role select "Classic Virtual Machine Contributor"

RDP Access to Virtual Machine
Start the virtual machine and add a local user to Windows.
Add the user to the list of approved users for RDP (http://windows.microsoft.com/en-us/windows/remote-desktop-connection-faq#1TC=windows-7).
Follow the steps here to give the user access to the virtual machine via Azure: https://azure.microsoft.com/en-us/documentation/articles/virtual-machines-windows-reset-rdp/