Assuming you are using jQuery UI,
Step 1 - Add an text input for your autocomplete:
<input type="text" id="search" />
Step 2 - Convert your DOM to a list of links:
var items = [];
$('ul li a').each(function () {
items.push({
value: $(this).attr('href'),
label: $(this).text()
});
});
$('ul').remove();
Step 3 - Turn on the autocomplete:
$("#search").autocomplete({
source: items,
select: function (event, ui) {
window.location.href = ui.item.value;
}
});