At first you need to enable remote desktop for your cloud service.
This can be done at least in two ways:
- During deployment from Visual Studio.
- Directly at the portal.
I think good way for you know is a second variant.
- Go to your cloud service.
- Enter Configure tab and press 'Remote' button at the bottom.
- Set all the needed settings there (role, user name, password, certificate, expiration etc.).
- After Azure finishes setup - go to 'Instances' tab. Click on the needed and 'Connect' button will be available.