使用AJAX，CSHTML发布表单

Question

trying to understand all this about AJAX, first of all I wanted to know how to refresh a page and keep my position on the page, which was possible, however, that was not the case on form post, that just jumped me right back to the top.

So after searching around on how to solve that, posting with AJAX seems to be my solution, I just can't seem to get all of it.

<form method="post" action="~/getAJAX.cshtml" id="ajaxform">
        <input type="text" name="kg" id="kg"  />
        <input type="submit" />
</form>
<script type="text/javascript">
    $(function () {
        $('#ajaxform').submit(function (event) {
            event.preventDefault(); // Prevent the form from submitting via the browser
            var form = $(this);
            $.ajax({
                type: form.attr('method'),
                url: form.attr('action'),
                data: form.serialize()
            }).done(function (data) {
                // Optionally alert the user of success here...
            }).fail(function (data) {
                // Optionally alert the user of an error here...
            });
        });
    });
</script>

This is the code I have so far. The thing I do not understand is what exactly should be on my "action" page?

At the moment I put this on my action page.

var db = Database.Open("Database");

var getKG = Request.Form["kg"];

var query = "SELECT * FROM Test WHERE kg = @0";
db.Execute(query, getKG);

This is just a test, I don't really know what to expect or anything, I would like to show the results on the page I post from, any guiding for this please?

Note that this is not a MVC project, therefore my problems with finding any good solutions or help, it's just normal CSHTML files.