<span id="like" class="glyphicon glyphicon-thumbs-up" ></span>
<span  id="dislike" class="glyphicon glyphicon-thumbs-down" ></span>

$(document).ready(function(){
    $("#like").click(function(){
           $("#like").addClass("green");
           $("#dislike").removeClass("red");
        });
  });
 $(document).ready(function(){
     $("#dislike").click(function(){
        $("#dislike").addClass("red");
            $("#like").removeClass("green");

        });
   });

// пишем
localStorage.setItem("someVal", "val");
// читаем
console.log( "someVal = " + localStorage.getItem("someVal"));