How to use Jquery to retrieve ajax search results for wordpress

You should wrap your code in document.ready

$(document).ready(function(){    $("#searchsubmit").click(function(e){        e.preventDefault();        var search_val=$("#s").val();         $.post(search.php,{search_string:search_val},function(data){            if(data.length>0){                $("#results").html(data);            }        });    });   });

Update:

$(document).ready(function(){    $("#searchsubmit").click(function(e){        e.preventDefault();        var search_val=$("#s").val();         $.ajax({            type:"POST",            url: "./wp-admin/admin-ajax.php",            data: {                action:'wpa56343_search',                 search_string:search_val            },            success:function(response){                $('#results').append(response);            }        });    });   });

In your functions.php

add_action('wp_ajax_nopriv_wpa56343_search', 'wpa56343_search'); // for not logged in usersadd_action('wp_ajax_wpa56343_search', 'wpa56343_search');function wpa56343_search(){    // code}

You can use the typeahead.js jquery plugin too, read this complete tutorial for more information:

http://wp.tutsplus.com/tutorials/plugins/enhancing-the-search-form-with-typeahead-js/