In a previous post I referenced instructions for installing BizTalk 2013 on Windows Azure. I also installed Microsoft Dynamics CRM 2013 on a virtual machine on Windows Azure. I found this post on survivingcrm blog to be extremely helpful. Here is a direct link to the slideshare instructions referenced on the blog post.

I did experience a couple of issues as explained here.

1. On slide 46 the CRM Reporting Extensions setup dialog is shown. This dialog did not appear for me so I run the setup manually which is located at c:\Users\crm_admin\SrsDataConnector\Microsoft.Crm.Setup.SrsDataConnector.exe

2. Once the installation was complete and running the site in IE, the site displays with the mobile theme. At the time of writing Microsoft are working on a fix. A work around for now is to ensure you navigate directly to the /main.aspx page on desktop systems.
So, if your CRM URL is http://mysite.com/organisationname then the URL to use would be http://mysite.com/organisationalunit/main.aspx

Another option instead of using Windows Azure is to create a trial on CRM Online as described here.