You can start developing Office and SharePoint apps with Windows Azure integration easily.
You can navigate to Start building apps for Office and SharePoint and Sign up for an Office 365 Developer Site.
With your Office 365 Developer Site, you get an isolated app domain for SharePoint-hosted apps, preconfigured to use OAuth, so that you can use the Windows Azure Access Control Service (ACS) for authenticating and authorizing provider-hosted apps for SharePoint that are deployed to this site.
Now, you have a test environment for starting development for Microsoft Office 3s65 with Windows Azure.
It's good for developing productivity applications that'll work with Office 365.