This is everything you need to register a servicestack service in Sitefinity. Just set your Route, and make sure to register the plugin!

SitefinityServiceStackTemplate.cs

using System;
using System.Collections.Generic;
using System.Linq;
using Telerik.Sitefinity;
using Telerik.Sitefinity.Model;
using Telerik.Sitefinity.DynamicModules;
using Telerik.Sitefinity.Data.Linq.Dynamic;
using Telerik.Sitefinity.Services.Search;
using Telerik.Sitefinity.Utilities.TypeConverters;
using ServiceStack.Text;
using ServiceStack;
using Telerik.Sitefinity.DynamicModules.Model;

namespace SitefinityWebApp.Services {
#region PLUGIN

    public class HelloServicePlugin : IPlugin {
        /// <summary>
        /// In Global.asax.cs in Application_Start make sure to call the SystemManager.RegisterServiceStackPlugin(new SitefinityWebApp.Services.HelloServicePlugin());;
        /// </summary>
        public void Register(IAppHost appHost) {
            appHost.RegisterService(typeof(HelloService));
        }
    }

    #endregion

    #region SERVICE
    public class HelloService : ServiceStack.Service {
        public object Get(HelloRequest request)
        {
            return "Hello {0}".Arrange(request.Name);
        }
    }
    #endregion

    #region REQUEST
    //This is available at https://<domain>/RestApi/myservice/hello
    [Route("/myservice/hello")]
    public class HelloRequest : IReturn<string>
    {
        public string Name { get; set; }
    }
    #endregion
}