Last week I blogged about developing a High-Availability plan. The specifics of a given plan aren't as simple as "Step 1, then Step 2" because in a hybrid environment (which most of us have) the situation changes the requirements. There are those that look for simple "template" solutions, but unless you settle on a single vendor and a single way of doing things, that's not really viable.
The same holds true for support. As I've mentioned before, I'm not fond of the term "cloud", and would rather use the tem "Distributed Computing". That being said, more people understand the former, so I'll just use that for now. What I mean by Distributed Computing is leveraging another system or setup to perform all or some of a computing function. If this definition holds true, then you're essentially creating a partnership with a vendor to run some of your IT - whether that be IaaS, PaaS or SaaS, or more often, a mix. In your on-premises systems, you're the first and sometimes only line of support. That changes when you bring in a Cloud vendor.
For Windows Azure, we have plans for support that you can pay for if you like. http://www.windowsazure.com/en-us/support/plans/ You're not off the hook entirely, however. You still need to create a plan to support your users in their applications, especially for the parts you control. The last thing they want to hear is "That's vendor X's problem - you'll have to call them." I find that this is often the last thing the architects think about in a solution.
It's fine to put off the support question prior to deployment, but I would hold off on calling it "production" until you have that plan in place. There are lots of examples, like this one: http://www.va-interactive.com/inbusiness/editorial/sales/ibt/customer.html some of which are technology-specific.
Once again, this is an "it depends" kind of approach. While it would be nice if there was just something in a box we could buy, it just doesn't work that way in a hybrid system. You have to know your options and apply them appropriately.