On the offers page (http://www.microsoft.com/windowsazure/offers/) you get a list of options you have to buy computing power on the Windows Azure platform.
As an MSDN Subscriber, I’m obviously first activating the benefits I get through my subscription. The process also includes providing credit card details but you won’t be charged unless you go over a certain amount of usage.
31 (days) * 24 (hours) = 744 hours. So it seems I can keep a small app running 24/7 for at least the next 8 months.