If you cannot connect to an Azure VM using RDP, ensure that you are using the correct credentials, and then follow the solutions provided here.

Organizations can now use their Azure Active Directory credentials to log into a Linux-based VM running on Microsoft's Azure public cloud service.

Here's a look at Azure Bastion, for securely connecting to Windows and Linux VMs, and Azure Lighthouse, which lets service providers deliver managed services for their customers .

With Linux running two out of five server instances on Azure, it's past time to learn how to do a good job of running Linux on Microsoft's Azure cloud ...

A platform-wide update now allows Windows and Linux VMs on Azure to reach networking throughput speeds of up to 25 Gbps, and Accelerated Networking hits GA for Windows, public preview for Linux.

Once the VM has been deployed, click Connect on the dashboard and you'll be offered to download an RDP file (had this been a Linux VM, an SSH connection would be offered instead).