Windows Azure is Microsoft public cloud platform, on which users can quickly build, deploy and manage Windows/Linux virtual machines, applications and websites across a global network of Microsoft managed datacenters.
Now let me take my first bite of it – build a Joomla website in the Azure cloud.
First, register a Azure account. You will be asked to provide your live account, phone number and credit card info.
Second, go to Portal/ WEB SITE/ FROM GALLERY.
Choose Joomla from the list.
Third, type in the following information choose click Next to build the Joomla website.
My Joomla website is up and running in the cloud now!! How easy it is 
Click BROWSE to view my new Joomla website.
To develop the website, you need to install the WEBMATRIX.
WebMatrix downloads the site to your local computer. You can develop the site locally, then publish it until you are satisfied with it.
WebMatrix will install any dependencies for you.
Jackie Chen's IT Workshop 
Thanks for this, just what I needed. I’ll go try installing Joomla now and see what happens. What confuses me a little bit is that I received already detail of a MySQL database (with host, user and password information) from a tech support person. I’m a bit worried if I can input this information correctly while installing Joomla to Azureus.
You should be able to, just choose to connect to an exisiting DB instead of create a new one in this step https://jackiechendotorg.files.wordpress.com/2012/08/image55.png