Node.js send data to backend with AJAX

I'm quite new to AJAX, so sorry for potential missunderstandings, but I'm not completely through that thing.

I'm trying a simple thing. I have a server.js file, which is my backend basically. Then I have a index.html and a script.js. That's all, so a very basic setup. Now, on my script.js, I'm getting some data (a mail address). Now I want to send that data to my backend (into the server.js) to work with it there. How can I do this?

I found some posts already about AJAX with node.js, but I don't get it, especially not where to receive it in my backend. I'm using express for the server by the way.

What I have in my script.js is:

$.ajax({
            type: "POST",
            url: "server.js",
            data: { mail: mail },
            success: function(data) {
            },
            error: function(jqXHR, textStatus, err) {
                alert('text status '+textStatus+', err '+err)
            }
        });

Right so far? How can I now receive the information in my server.js?

There's not much in so far, just:

var express = require('express');

var app = express();
var server = app.listen(3000);

app.use(express.static('public'));

Thanks for any help :)