I have been thinking about writing a post about this for a long time. However now a new whitepaper was released that explains how to configure a BI environment in Azure. It is called SharePoint Deployment on Windows Azure Virtual Machines and describes the steps in detail. You can find the paper here:

http://www.microsoft.com/en-us/download/details.aspx?id=34598

I may revisit this post in the future to show how you can set up your own demo/test environment in the cloud.