client.html

<script>
    $(document).ready(function () {
      
        $("#btnLogUser").click(function () {
            $.ajax({
                type: "POST",
                url: 'api/test/',
                error: function (msg) {
                    alert("Error !: " + msg);
                },
                success: function (data) {
                    console.log(data);

             

                }
            });
        });

        $("#AuthrizeAction").click(function () {
            $.ajax({
                type: "GET",
                url: 'api/test/',
                error: function (msg) {
                    alert("Error !: " + msg);
                },
                success: function (data) {
                    console.log(data);

                }
            });
        });

    });

</script>

<button id="AuthrizeAction">is Authorize ?</button>

<button id="btnLogUser">log</button>

TestController.cs

        // POST api/test
        //Action log user 
        public object Post()
        {
            var success = Membership.ValidateUser("tomadj", "thomas");

            if (success)
            {
                FormsAuthentication.SetAuthCookie("tomadj", true);
                return new { success = true, redirect = "" };
            }
            else
            {
                return new { success = false, redirect = "" };
            }
        }
        
                // GET api/test
                //Authorize action 
        [Authorize]
        public IEnumerable<string> Get()
        {
            return new string[] { "value1", "value2" };
        }