To host application in cloud computing
you upload your application to Azure using the Azure portal at:
If you're wanting to put a SQL database back end in the cloud, you'll want to check out SQL Data Services. If you want to access your on premise SQL Server from the cloud you'd have to punch in the appropriate holes into your firewall to allow access (not something I think any DBA or network admin would be fond of doing).
You might want to check out the Windows Azure whitepaper from MS. It has alot of introductory type information on the services available as part of Azure Services: http://www.microsoft.com/azure/whitepaper.mspx
I've also posted several blog articles that walk through some basic topics: http://bstineman.spaces.live.com/?_c11_BlogPart_BlogPart=blogview&_c=BlogPart&partqs=cat%3dAzure%2520Services
Cloud computing can be broken down into 3 basic categories.
SaaS - software as a service (using a hosted product such as SalesForce.com or CRM Online)
PaaS - creating an application that is then deployed into a hosted environment (Windows Azure)
IaaS - a virtualized infrastructure hosted in the cloud (EC2 and to an extent Windows Azure)
When hosting an application in Azure, it needs to be built for Windows Azure. You can't simply build it as you would a traditional on-premise application and push it up to the cloud. This doesn't prevent you from pushing custom bits into Azure as you did with an on-premise but it does limit what can be pushed. In a nutshell, it seems that if you have to run an install to get require software on the computer, you won't be able to run it on Azure. However, if you just need to load some redistributables onto the box and they can reside in the application folder, that shouldn't prohibit it running.
Course as you'd expect, there are security limitations in place to help ensure that anything that gets loaded into your deployment don't compromise the Azure Fabric and possibly damage other applications running in the Windows Azure cloud.