How do you add a mime type when using ASP.NET vNext?

If you hosting it on IIS 7 or later then following step will do what you need. This answer I have used Visual Studio 2015 CTP5.

1. Publish your web application ( ASP.net vnext)
2. You can publish it to location like C:\MyPublish
3. Once it get successfully published you will find following location C:\MyPublish\wwwroot. Here You will find web.config.
4. Now host your site to in IIS ( Make sure that you have used C:\MyPublish\wwwroot as your path)
5. Now edit web.config over here just like you did for old version to add mime type. ( Following is my edit)

  <?xml version="1.0" encoding="utf-8"?>
   <configuration>
  <appSettings>
    <add key="kpm-package-path" value="..\approot\packages" />
    <add key="bootstrapper-version" value="1.0.0-beta2" />
    <add key="kre-package-path" value="..\approot\packages" />
    <add key="kre-version" value="1.0.0-beta2" />
    <add key="kre-clr" value="CLR" />
    <add key="kre-app-base" value="..\approot\src\WebApplication5" />
  </appSettings>
    <system.webServer>
        <staticContent>
            <remove fileExtension=".woff" />
      <mimeMap fileExtension=".woff" mimeType="application/font-woff" />
        </staticContent>
    </system.webServer>
</configuration>

Note: As per my thinking In old version it is fix that it is always windows environment so we have direct web.config file in project and we edit that but now we have to follow different process to register as in future we can host completly on linux env as well.

Update : There is another way to do that as well. If you are using Microsoft.AspNet.StaticFiles package then you will have extension.

public void Configure(IApplicationBuilder app)
        {
            app.UseStaticFiles();
        }

This will indirectly use https://github.com/aspnet/StaticFiles/blob/dev/src/Microsoft.AspNet.StaticFiles/FileExtensionContentTypeProvider.cs. Here you can see all mapping.

Update 2: (Add New Mime Type)

 public void Configure(IApplicationBuilder app)
            {
                StaticFileOptions option = new StaticFileOptions();
                FileExtensionContentTypeProvider contentTypeProvider = (FileExtensionContentTypeProvider)option.ContentTypeProvider;
                contentTypeProvider.Mappings.Add("<<yourextention>>","<<mimetype>>");
                app.UseStaticFiles(option);
            }