How to connect to Linux VM in Azure.

You cannot connect to Linux VM using windows remote desktop connection (RDP) by default.
To connect to Linux VM on azure you will need to make use of Putty.
Putty is available on

Login in to Linux using the Linux vm IP address

Use putty to connect to Linux VM. enter your user name and password.

Enable Linux Unity Desktop Interface.

Unity desktop is not enabled when you provision a Linux box in Azure.
To enable Linux interface issue the following command on Linux prompt
sudo apt-get update
sudo apt-get install ubuntu-desktop

This will take around 15 to 30 minutes to finish.

Install XRDP on your Linux box

$ sudo apt-get install xrdp

Add Azure RDP Endpoint Port 3389 on both  public and private port.

This will allow you to connect to Linux desktop via windows RDP interface

RDP your Linux VM.

Next step is to RDP your Linux VM. When you login to Linux box it will prompt you with this

Login to Linux Desktop

The last step is to login to your Linux desktop.