I started going through the Azure SDK and samples last night and got tripped up on a few issues. Here are some of the steps to get started with the basics of Azure development:
1. To get started, you'll need Visual Studio 2008 with SP1 and make sure you also have SQL Server 2005 (or 2008) Express installed with the SQLEXPRESS instance name. The SDK samples require this.
2. Install the Azure SDK from http://www.microsoft.com/downloads/details.aspx?FamilyId=BB893FB0-AD04-4FE8-BB04-0C5E4278D3E9&displaylang=en.
3. Install the Azure Tools for Visual Studio from http://www.microsoft.com/downloads/details.aspx?FamilyId=63D0D248-1B08-4F7D-ABDE-62EB75CB1E69&displaylang=en. Not required to run the SDK samples but you will need to install it to run the hands on lab.
4. Read this page, http://msdn.microsoft.com/en-us/library/dd179419.aspx. The RunDevStore.cmd step is critical because if this fails then nothing else will work. There will be a yellow warning once it gets to the end but you can disregard this. Just make sure there are no red errors.
5. Download, build and run the hands on lab sample from this page, http://mbrownchicago.spaces.live.com/blog/cns!2221DC39E0C749A4!1040.entry?wa=wsignin1.0. It probably will build correctly but throw a runtime error saying that it could not find the Microsoft.ServiceHosting.ServiceRuntime assembly. For some reason this assembly is not installed in the SDK's bin folder but in a ref folder. You can either copy the assembly into the bin folder or add the ref folder into your machine's PATH environment variable.
6. Finally, it probably goes without saying, but run everything with administrative rights.
If all goes well then this is what you should see when you run the hands on lab, with the Development Fabric UI running in the background.

In addition to the samples and hands on lab, you can also learn more about Azure development from online videos such as here, here and here.