using System;
using System.Net.Http.Formatting;
using System.Web.Http;

namespace Feature.DataAPI
{
    public static class WebApiConfig
    {
        public static void Register(HttpConfiguration config)
        {
            // Web API configuration and services

            // This block of code sets the application to emit json globally by default
            GlobalConfiguration.Configuration.Formatters.JsonFormatter.MediaTypeMappings.Add(
                new RequestHeaderMapping("Accept", "text/html", StringComparison.InvariantCultureIgnoreCase, true,
                    "application/json"));
        }
    }
}

using System.Web.Http;

namespace Feature.DataAPI
{
    public class WebApiApplication : System.Web.HttpApplication
    {
        protected void Application_Start()
        {
            GlobalConfiguration.Configure(WebApiConfig.Register);

            // This block of code is to handle a circular reference error when serializing the json output
            GlobalConfiguration.Configuration.Formatters.JsonFormatter.SerializerSettings.ReferenceLoopHandling =
                Newtonsoft.Json.ReferenceLoopHandling.Ignore;

            GlobalConfiguration.Configuration.EnsureInitialized();
        }
    }
}

using Sitecore.Pipelines;
using System.Web.Http;
using System.Web.Http.Routing;

namespace Feature.DataAPI.Pipelines
{
    public class RegisterRoutes
    {
        public void Process(PipelineArgs args)
        {
            GlobalConfiguration.Configure(Configure);
        }

        private static void Configure(HttpConfiguration configuration)
        {
            configuration.Routes.Add("API", new HttpRoute("sitecore/api/{controller}/{id}"));
        }
    }
}

<configuration xmlns:patch="http://www.sitecore.net/xmlconfig/">
  <sitecore>
    <pipelines>
      <initialize>
        <processor type="Feature.DataAPI.Pipelines.RegisterRoutes,Feature.DataAPI" patch:after="processor[@type='Sitecore.Pipelines.Loader.EnsureAnonymousUsers, Sitecore.Kernel']" />
      </initialize>
    </pipelines>
  </sitecore>
</configuration>