Send AJAX request by clicking a link without redirecting user

You have to do something like

$('.classofyourlink').click(function(e){
  e.preventDefault();//in this way you have no redirect
  $.post(...);//Make the ajax call
});

in this way the user makes an ajax call by clicking a link without redirecting. Here are the docs for $.post

EDIT - to pass the value to jQuery in your case you should do something like

$('.order_this').click(function(e){
  e.preventDefault();//in this way you have no redirect
  var valueToPass = $(this).text();
  var url = "url/to/post/";
  $.post(url, { data: valueToPass }, function(data){...} );//Make the ajax call
});

HTML

<a id="aDelete" href="mypage.php">Delete</a>

Script

$(function(){    
   $("#aDelete").click(function(){           
      $.post("ajaxserverpage.php?data1=your_data_to_pass&data2=second_value",function(data){
         //do something with the response which is available in the "data" variable
     });
   });
  return false;    
});