What you need to do is look at the application from the Microsoft DNA method, using the 3 tiered approach.
You have a presentation layer
business logic layer
application data layer.
In this method you would treat the web side the same as your forms in vb. To do this all of the functionality of the program must be in the classes and not in the forms.
If your asking "Can I take my existing VB ap and with a little magic make it Webified?" the answer is with a lot of magic.
You will have to separte your presentation layer from the ap, and then create a dll (create a dll project then add your existing classes) to support it.
Your presentation layer now becomes your ASP or HTML files, they call the VB.DLL to do all the work.
It's a very nice method of doing things, but you have be regimented in programming it so that all of the business logic is in the business logic layer and not have any of it in your presentation layer (VB Forms or HTML Pages)