There are three services to sign up for: Windows Azure, .NET Services and SQL Data Services. You sign-up for all of these services here: http://go.microsoft.com/fwlink/?LinkID=129453
You will NOT receive your tokens immediately. It make take awhile. Also, there are different tokens for different services and they may arrive at different times. This can be confusing, but basically you just need to be patient. You will need TWO invitation tokens to receive access to all three services.
Windows Azure - provides computation services, hosting for ASP.NET applications and access to Azure Storage (blob, queue & table). Requires invitation token with the form XXXXX-XXXXX-XXXXX-XXXXX-XXXXX, where 'X' is [0-9A-F]. Access via the following URL: http://lx.azure.microsoft.com/fs
.NET Services & SQL Data Services - provides access to Service Bus, Access Control Service, Workflow Service and SQL Data Services. Requires invitation token with the form: XXX-XXXX-XXXX, where 'X' is [0-9A-Z]. Access via the following URL: http://portal.ex.azure.microsoft.com/
Please note, Azure Storage != SQL Data Services. Azure Storage provides rudimentary database support via the table storage. SQL Data Services provides more conventional database concepts.