There are a number of ways to create an editable 404 message. I've bee using the current solution for some time know. Based on this old post: http://world.episerver.com/Forum/Developer-forum/EPiServer-7-CMS/Thread-Container/2013/3/Custom-404-page-in-EPi-7-MVC/

Web.config

<system.webServer> 
  <httpErrors errorMode="Custom" existingResponse="Auto">
      <remove statusCode="404" />
      <error statusCode="404" responseMode="ExecuteURL" prefixLanguageFilePath="en" path="/NotFound" />
  </httpErrors>
....

<system.web>
  <customErrors mode="On">
      <error statusCode="404" redirect="/NotFound"/>
  </customErrors>
...

Controller

Add this Method to your "default" page controller.

public ActionResult NotFound(PageData currentPage)
        {
            var startPage = ContentReference.StartPage.Get<StartPage>(); 
            // Set RoutingConstants.NodeKey so EPi's extension method RequestContext.GetContentLink() will work
            ControllerContext.RouteData.DataTokens[RoutingConstants.NodeKey] = startPage.PageLink;

            Response.StatusCode = 404;
            ViewBag.Is404 = true;
            return View($"~/Views/Pages/{startPage.GetOriginalType().Name}.cshtml", startPage);
        }
    }

As you can see I'm using the view for the startpage to show the 404-message. The view checks if ViewBag.Is404 and displays an error message in a lightbox. There is no separate 404-page, the error message is edited on the start page.

Hope this helps! 

Note that this is a stripped down version of how I'm doing it, might have missed something when removing code

I prefer doing a static 404 html page actually and use that if it doesn't have to be dynamic (depending on what you were trying to reach). Reason is basically that I've seen quite a few sites crash because you end up in an infinite loop of 404s in some cases. That combined with that 404 page is almost never changed => old school html page is not a bad idea actually. 

Last time I checked the BVNetwork extension was a good and maintainable feature to use:

https://github.com/BVNetwork/404handler

I have a site which is published in English and Danish. I have implemented the error page as follows.

Web.config:

<system.webServer> 
  <httpErrors errorMode="Custom" existingResponse="Auto">
      <remove statusCode="404" />
      <error statusCode="404" responseMode="ExecuteURL" prefixLanguageFilePath="en" path="/NotFound" />
  </httpErrors>

Global asax:

RouteTable.Routes.MapRoute(
                "NotFound",
                "NotFound",
                new {controller = "NotFoundPage", action = "Index"});

NotFoundPageController:

public ActionResult Index(PageData currentPage)
        {
            var notFoundPage = GlobalProperties.HomePageReference().Settings.NotFoundPage.GetContent<NotFoundPage>();

            // Set RoutingConstants.NodeKey so EPi's extension method RequestContext.GetContentLink() will work
            if (notFoundPage != null && ControllerContext?.RouteData != null)
            {
                ControllerContext.RouteData.DataTokens[RoutingConstants.NodeKey] = notFoundPage.PageLink;
            }

            if (Response != null) Response.StatusCode = 404;

            return View(new DefaultViewModel<NotFoundPage>(notFoundPage));
        }

My problem is that the 404-page is not presented in the correct language. I have checked that the error page is created and published in both languages inside Episerver but it always returns the Danish page (Danish is default language). This the case if I go to http://mysite/unknown-page or http://mysite/da/unknown-page or http://mysite/en/unknown-page.

Am I missing something in the config file that should pass the language to the NotFoundPageController or is it something else?

Thanks for the tip, Sebastian!

The BVNetwork 404 Handler (https://nuget.episerver.com/en/OtherPages/Package/?packageId=BVN.404Handler) lets you redirect to any page in your CMS. You can then set up a page (call it "404" or something), and let the 404 handler send the visitor there when the page is not found in the page tree. As Daniel points out, this might throw you into an infinite loop, e.g. when what is missing is the page logo, and this logo is also used on your 404 page...