This is a complicated question because you can use VB6 to write .dll files that can be utilized within an ASP page.
Since I assume you are talking about converting the interface itself, I will say there is no easy way to do this with an automatic process. You would have to redesign all your screens\forms in HTML\ASP pages.
From that point you can retain functions from your original VB6 program and just cut and paste them into your ASP pages, but they may end up being called or used in different ways within the web environment.
I would recommend designing your interface in the web first, then start trying to identify code you may be able to directly move from your app to your pages.
One of the more difficult parts of this conversion for you will likely be the validation of data on any forms you have, because in a web environment this validation needs to be done using javascript if you want it to execute in the users browser immediately (like checking for numeric values, etc)
Go here to start out and post specific problems as you run into them when your migrating your application.
http://www.w3schools.com/asp/default.asp
If you want to use ASP.NET that is a totally different animal but the same basic concepts apply. You would need to re-design your interface in the web, and move whatever functions you can move over into your pages.
http://www.w3schools.com/ASPNET/default.asp 
