I followed these instructions to deploy to Azure:
And it actually worked, but I get a Guid for a Website URL. How can I hook it up to an Azure website? Something like patrickinmpls.azure.com ?

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Adding to @mfanto’s comment, you would need to publish your application to production slot and then you’ll get a yourservicename.cloudapp.net URL which you can then map to your custom domain name. See this link for more details: http://www.windowsazure.com/en-us/develop/net/common-tasks/custom-dns/.