+2  A: 

You basically need an ajax call made each time the value of the textbox changes.

Totally untested, but something along the lines of:

$("#inputName").change(function () {
    // maybe check the value is more than n chars or whatever
    $.ajax({
        url: <%= Url.Action("Lookup", "Users") %> + '/' + this.val(), // path to ajax request
        dataType: "html", // probably
        success: updateContainerWithResults
    });
});

function updateContainerWithResults(data) {
    $("#resultsContainerElement").html(data);
}

http://docs.jquery.com/Events/change

http://docs.jquery.com/Ajax

Sam Wessel
FYI `change` only fires on blur of the textbox, not on every keystroke.
Crescent Fresh
So what event should be used then for each keystroke?
keyup. However, you might want to take a look at some of the autocomplete jquery functions. You'd have to modify them to suit your needs, but they offer some improvement. Ie, if someone is typing john, and they type 'j', do you really want to search for all users with the letter j? If they type j-o-h-n really quickly, do you really want to send 4 separate requests to the server?
James S
@crescentfresh in ie yeah.
redsquare
@redsquare: `<input type="text" />` fires change on blur or submit of the parent form (if any). See http://www.quirksmode.org/dom/events/change.html . What browsers do you see this behavior *not* happen? Curious...
Crescent Fresh