Experience Sitecore !

Here is the code that creates a route for you. In global.asax.cs you will call RegisterRoutes from App_Start event handler:

    protected void Application_Start()
    {
        RouteConfig.RegisterRoutes(RouteTable.Routes);
    }

And there you specify your route as:

    public static void RegisterRoutes(RouteCollection routes)
    {
        routes.MapRoute(
             name: "test",
             url: "mvc/Forms/{action}/{id}",
             defaults: new { controller = "Forms", action = "Test", id = UrlParameter.Optional }
           );
    }

You will have /mvc/ prefix in this case that will handle your route to specifies controller, so you will call it as:

/mvc/Forms/Test/{you_may_pass_some_optional_GUID_here}

This will route to FormsController class action method Test(string id) but you may omit id parameter

A bit of attention: Please note that setting route in Application_Start is not the best way of doing that; much better is to implement mapping routes at Initialize pipeline, as it fits Sitecore architecture:

public class Initialize
{
    public void Process(PipelineArgs args)
    {
        MapRoutes();
    }

    private void MapRoutes()
    {
        RouteTable.Routes.MapRoute(
                "Forms.Test", 
                "forms/test", 
                new
                {
                    controller = "FormsController",
                    action = "Test"
                },
                new[] { "Forms.Controller.Namespace" });
     }
}

The rest of implementation: Also I have previously wrote an article in my blog about how to implement ajax call to a route, that will guide you through the rest of the implementation process:

https://blog.martinmiles.net/post/editing-content-on-a-cd-server

Update: Please also make sure your config has a handler to handle your prefix, see below:

<customHandlers>
    <handler trigger="~/mvc/" handler="sitecore_mvc.ashx" />