As per the MS release, the azure usage is to be calculated based on the 'compute instance'. $0.12 per hour it appears is for the 'small compute' instance size. For others, multiply this by the number of CPUs as per the below image :
Caveats
Based on your requirement, you could go for the small/medium/Large/Extra Large instance size. Things sound good until we dig a bit deeper on this. There are a couple of weird bits about the compute metering:
1.) If your application instance has 10 roles (worker/web...), each role would add up to the hrs!
Eg: - if you have 10 roles active simultaneously for 1 hr, you are charged for 10hrs.
2.) There is no part calculation. Even if you had you application active in Azure for 5mins and you delete it , you would end up paying charge for 1 hr!. This also is effective for the roles:
Eg: - if you have 10 roles active simultaneously for 5minutes, you are charged for 10hrs (yes, 10hrs)
3.) The compute usage is not determined by the actual computing/processing usage. Say even if your role/instance is idle for 50mins in the 1 hr, you are still charged for 1hr! This means that as soon as you have your application deployed, you get billed - immaterial of its computing usage.
Simplifying it down, your usage charge for a month = Number of roles in your instance * 24 (hrs in a day) * 31 (days in a month) * Subscription-factor.
Where, Subscription-factor = 1 for small, 2 for Medium,4 for Large , 8 for Extra large.
4.) Another interesting bit is about the alignment with the hours - it appears if you deploy your application at 3:50pm, you would have to pay an additional hours charge (2pm-3pm, 3pm-4pm).
5.) Are you a developer? There is no developer account/scheme wherein you could test out your application in Azure for free, yet.
Anything that adds to the MS revenue is good (for them).
Update 15.05.2010
For the various queries raised in this regard to the Azure support team, the answers from them haven't been direct, but rather confusing. Please do not rely on this post for deducing the cost, but contact the Azure team directly.