On the page which has the search engine, ensure onkeyup="autocomplet()" is in the input form.

<form>
    <input type="text" is="search_id" onkeyup="autocomplet()">
</form>

This is the JavaScript.

function autocomplet() {
	var min_length = 0; // min caracters to display the autocomplete
	var keyword = $('#search_id').val();
	if (keyword.length >= min_length) {
		$.ajax({
			url: 'ajax_search_processing.php',
			type: 'POST',
			data: {keyword:keyword},
			success:function(data){
				$('#search_results').show();
				$('#search_results').html(data);
			}
		});
	} else {
		$('#search_results').hide();
	}
}

function set_item(item) {
	// change input value
	$('#search_id').val(item);
	// hide proposition list
	$('#search_results').hide();
}

This is the SQL stuff.

<?php
$con = new mysqli('ip_domain','username','password','database');
$keyword = $POST['keyword'];
$sql = "select * from tablename where name like '%$keyword%' ";
$sql_query = mysqli_query($con,$sql);

while ($row = mysqli_fetch_array($sql_query)) {
echo $row['data'];
}
?>

<div id="search_results"></div>