Quite alot if you want the windows forms to actually open from a page or link on a user's web browser. You'd have to either; convert the VB standalone application to an ActiveX application, and use that on the webpage, but be warned, clientside ActiveX only works on Microsoft's web browsers and VB only really works under Windows. Still, you could convert the application in that way very simply; since you could reuse pretty much all the code with a few changes at the entry point of the application; and then add it to webpages with a tiny bit of ( MS only ) HTML code.
http://www.geocities.com/SiliconVall...50/ActiveX.htm
[this is for the old VB; but I imagine the same principles apply today.. although doing the necessary things might require different actions to be taken]
Alternatively, you could rewrite the application as a Java applet, Java is more widely supported than VB, and can do much the same form-based things as VB; it'd be a bit of work, but, IMHO it's the best option here. Alternatively, write it again in Javascript; although, it'd be more difficult to rewrite most VB apps in JS than it would to rewrite them in Java, and JS has no 'forms' framework, at least not for the kind of forms you're talking about. Alternatively, allow the user to download your application; and run it on their desktop. There's nothing to stop you making HTTP connections from your app, which would give you the ability to do everything ( and probably more ) than you could do from an app running in any of the sandboxed ( i.e. highly restricted ) environments that all webpage-based applications are stuck in.
If the application isn't meant to be run at the user's end; i.e. it's a server application; then, I have no idea. I've never used a Windows server for anything more than HTML/basic ASP... but I'm sure it's possible to configure and use a VB app as a server program. It's certainly possible to write DLLs that can be used from other MS technologies, so, you could write a DLL in VB and perhaps use it from ASP... The user ( infact no-one ) will see the pretty forms though.