Getting started with Windows Azure isn't as tricky or daunting as you may think. After all, its familiar tools, with your end product (an application) residing in a different place. I'd concur with my colleague Tom Hollander who argued recently that the best way to learn new technologies is via a real or realistic assignment.
The following links are just ways in filling up your knowledge gaps. Its also worthwhile checking out instructor led events such as the RDN if you are like me in putting off training for another day, it might be worth considering Windows Azure platform Acceleration Technical Training Tour â Sydney 27th/28th January if you are in town.
If you haven't registered for an account you may want to start by using these step by step videos on how to register for Windows Azure.
There are various types of training to fill the gap:
Whatever your choice it may be worthwhile drawing up a learning plan (like Buck Woody's example) and signing up to one of the offers or discovery packs
A comprehensive and supersite for getting started in general can be found here