In order to serve static files in Asp.Net Core you will need following line in Startup.cs method configure:
app.UseStaticFiles();
When deploying in order to show default document, add following line:
app.UseDefaultFiles();
My whole Startup.cs looks like this:
using Microsoft.AspNetCore.Builder;
using Microsoft.AspNetCore.Hosting;
using Microsoft.AspNetCore.Mvc;
using Microsoft.Extensions.Configuration;
using Microsoft.Extensions.DependencyInjection;

namespace AllPics2gMaps
{
  public class Startup
  {
    public Startup(IConfiguration configuration)
    {
      Configuration = configuration;
    }

    public IConfiguration Configuration { get; }

    // This method gets called by the runtime. Use this method to add services to the container.
    public void ConfigureServices(IServiceCollection services)
    {
      services.AddMvc().SetCompatibilityVersion(CompatibilityVersion.Version_2_1);
    }

    // This method gets called by the runtime. Use this method to configure the HTTP request pipeline.
    public void Configure(IApplicationBuilder app, IHostingEnvironment env)
    {
      if (env.IsDevelopment())
      {
        app.UseDeveloperExceptionPage();
      }
      else
      {
        app.UseHsts();
      }

      app.UseHttpsRedirection();
      app.UseMvc();
      app.UseDefaultFiles();
      app.UseStaticFiles();
    }
  }
}
Title of this article I have took from here.

If you are receiving a message like:

Cross-Origin Request Blocked: The Same Origin Policy disallows reading the remote resource at http://test:2021/api/values. (Reason: CORS header ‘Access-Control-Allow-Origin’ missing)
This means that you have to enable CORS (since 2014)

In my case I have created new ASP.NET Core WebApi on the link http://test:2021/api/values, and I was accessing that link from http://gallery.milosev.com:9090.

Open Startup.cs:

First add line:

readonly string MyAllowSpecificOrigins = "_myAllowSpecificOrigins";
Then:
public void ConfigureServices(IServiceCollection services)
{
  services.AddMvc().SetCompatibilityVersion(CompatibilityVersion.Version_2_1);

  services.AddCors(options =>
  {
	options.AddPolicy(MyAllowSpecificOrigins,
	builder =>
	{
	  builder.WithOrigins("http://gallery.milosev.com:9090");
	});
  });
}
Here notice: http://gallery.milosev.com:9090, and at the end:
public void Configure(IApplicationBuilder app, IHostingEnvironment env)
{
  if (env.IsDevelopment())
  {
	app.UseDeveloperExceptionPage();
  }
  else
  {
	app.UseHsts();
  }

  app.UseCors(MyAllowSpecificOrigins);
  app.UseHttpsRedirection();
  app.UseMvc();
}
Whole Startup.cs:
using Microsoft.AspNetCore.Builder;
using Microsoft.AspNetCore.Hosting;
using Microsoft.AspNetCore.Mvc;
using Microsoft.Extensions.Configuration;
using Microsoft.Extensions.DependencyInjection;

namespace EnableCORS
{
  public class Startup
  {
    public Startup(IConfiguration configuration)
    {
      Configuration = configuration;
    }

    public IConfiguration Configuration { get; }

    readonly string MyAllowSpecificOrigins = "_myAllowSpecificOrigins";

    // This method gets called by the runtime. Use this method to add services to the container.
    public void ConfigureServices(IServiceCollection services)
    {
      services.AddMvc().SetCompatibilityVersion(CompatibilityVersion.Version_2_1);

      services.AddCors(options =>
      {
        options.AddPolicy(MyAllowSpecificOrigins,
        builder =>
        {
          builder.WithOrigins("http://gallery.milosev.com:9090");
        });
      });
    }

    // This method gets called by the runtime. Use this method to configure the HTTP request pipeline.
    public void Configure(IApplicationBuilder app, IHostingEnvironment env)
    {
      if (env.IsDevelopment())
      {
        app.UseDeveloperExceptionPage();
      }
      else
      {
        app.UseHsts();
      }

      app.UseCors(MyAllowSpecificOrigins);
      app.UseHttpsRedirection();
      app.UseMvc();
    }
  }
}
Here I explained how to publish code to IIS, and here I explained one way to debug your application, but I don't like it, since it is taking too much time to start. Here I have found another way to debug asp.net core application, from my point of view much better. Here I already explained hot to attach to process, the only difference ist that you have to attach to "dotnet.exe":

To write this article I was using Development-time IIS support in Visual Studio for ASP.NET Core.

First in Visual Studio installer enable development-time IIS support in Visual Studio:

Create new Asp.Net Core MVC application.

Add application to IIS, as physical path in my case I added "C:\Users\pera\Documents\Visual Studio 2017\Projects\WebApplication1\WebApplication1":

In Visual Studio right click on project go to properties:

Go to Debug, click on new:

In profile name write IIS:

Launch: IIS, Select the check box for Launch browser: http://test:2021/, the Environment variables section, select the Add button. Provide an environment variable with a Name of ASPNETCORE_ENVIRONMENT and a Value of Development:

Restart Visual Studio as administrator, if you haven't already.

Set the Start Debugging button to the IIS profile and select the button to start the app: