As is true with VB6 Windows applications, you have options when it comes to migrating VB6 ASP Web applications to ASP.NET. The first thing to point out is that ASP and ASP.NET applications can coexist. Thus it is worthwhile to evaluate whether to migrate at all. Microsoft also recommends reading "Migrating Your ASP Applications to ASP.NET" and "Migrating to ASP.NET: Key Considerations" before you migrate. Both of these articles are available at http://msdn.microsoft.com.
To get you started, here's an overview of the steps that will help you migrate to ASP.NET.
To keep it simple, if you change the names of your .asp files to .aspx files and open them in Visual Basic .NET, they will be treated as .aspx files. To make them more powerful you may want to migrate specific controls to Web server controls and add a code-behind file to the .aspx.vb file created by the IDE. However, simply renaming the extension will get you well under way.