How to convert a heavy software to a web application to use via cloud?

i didnt really got your question , but i think you need to convert the software to web application at first , the software it self must be built in fully object oriented language like asp.net you can create new view ( HTML , CSS ) for web and start to call that classes for cloud try this http://aws.amazon.com/what-is-cloud-computing/

You need to define what "heavy software" means.
Is that a desktop application? If so, you can, depending on your architecture, leverage some of your business logic and create a model layer.
For example, if you have code that returns user data as a dataset, you can use that in your Data Access Layer.
If you have code that updates a product price, that can go into your business logic layer, and so on.
The biggest change would be your view, where the web comes in.
Your aspx, php, or whatever you'll be using, will start calling your backend code via some view classes.
I'd strongly suggest you look at ASP.Net MVC framework if you're using .net.
As for the cloud, that is just a way of deployment, but that's a very broad subject.
You can look at Windows Azure service if you're looking for .Net.
If you want something that is platform-independent, you can look at Amazon EC2 where you can develop in any language but you need to do so on an operating system that supports EC2 (most OS today do) and just install on your virtual server.
For complete explanation see this http://aws.amazon.com/ec2/faqs/

If your software was designed with presentation and logic separation in mind, you might only edit very few things.

1- Compile your logic to a separate entity (ex: DLL).

2- You will just need to build some html pages, and used any web serve language (php, asp.net, ruby...) to call your complied logic libraries on the server and present output to the html files.

3- To publish on cloud, see the second part of Hazem Salama's answer in this thread.