ASP.NET is part of the .NET Framework, which should be installed. When you
look in Project Templates, you should see various web project types like
ASP.NET Web Application and ASP.NET Web Service. If these don't work for
you, did you install Internet Information Services (IIS) from your OS CD
prior to installing VS.NET 2003? If you didn't, then you'll need to follow
the instructions in Knowledge Base Article #306005, which addresses
repairing the mapping between VS.NET and IIS.
Here is a partial quote from the article:
"SUMMARY
                 After you install the Microsoft .NET Framework Software
                 Development Kit (SDK) or Visual Studio .NET, Microsoft
                 Internet Information Service (IIS) mappings are created to
                 associate the new file extensions and settings for
ASP.NET. If
                 you did not have IIS installed when you ran the SDK or
Visual
                 Studio Setup, or if you uninstalled and reinstalled IIS
after
                 you ran the SDK or Visual Studio Setup, those settings
will
                 not be in place. You experience unexpected behavior when
you
                 try to view ASP.NET pages.

                 When you try to create a new ASP.NET Web application in
Visual
                 Studio .NET 2003, you receive the following error message:

                 Visual Studio .NET has detected that the specified Web
server
                 is not running ASP.NET version 1.1. You will be unable to
run
                 ASP.NET Web applications or services.
                 MORE INFORMATION
                 To fix IIS mappings for ASP.NET, follow these steps:
                   Run the Aspnet_regiis.exe utility:
                     Click Start, and then click Run.
                     In the Open text box, type cmd, and then press ENTER.
                     At the command prompt, type the following, and then
press
                     ENTER:
                     "%windir%\Microsoft.NET\Framework\version\aspnet_regiis.exe"
                     -i
                     In this path, version represents the version number of
the
                     .NET Framework that you installed on your server. You
must
                     replace this placeholder with the actual version
number
                     when you type the command.
                   Register the Aspnet_isapi.dll:
                     Click Start, and then click Run.
                     In the Open text box, type the following, and then
press
                     ENTER:
                     regsvr32
                     %windir%\Microsoft.NET\Framework\version\aspnet_isapi.dll
                     Regsvr32 returns the results of the registration.
                 REFERENCES
                 For more information about the Aspnet_regiis.exe utility,
run
                 this .exe file with -? as an argument.

                 For a description of the symptoms that are typically
related
                 to ASP.NET and IIS application mappings that are not
                 configured properly, click the following article number to
                 view the article in the Microsoft Knowledge Base:
                 325093 PRB: ASP.NET Pages Exhibit Unexpected Behavior
Because
                 the Server-Side Code Is Not Processed "