Ajax tutorial for post and get

I need a simple ajax tutorial or case study for a simple input form, where I want to post a username through an input form, which sends it to the database and replies with the results.
Any recommendation for such tutorial is welcome, because I've only got one using Mootool but I'm searching for one using jQuery!

You can try this:

$.ajax({
  url: "test.html",
  cache: false,
  success: function(html){
    $("#results").append(html);
  }
});

This code will append the content of test.html file to #results element

You can find more information at jQuery website.

Update:

Use this code to send POST data and output result.

var menuId = $("ul.nav").first().attr("id");
var request = $.ajax({
  url: "script.php",
  type: "POST",
  data: {id : menuId},
  dataType: "html"
});

request.done(function(msg) {
  $("#log").html( msg );
});

request.fail(function(jqXHR, textStatus) {
  alert( "Request failed: " + textStatus );
});

Assuming you have some html like:

<input type="text" name="username" id="username">
<div id="resultarea"></div>

You would use a <script> like:

var myusername = $("#username").val();
$.ajax({
  type: "GET",
  url: "serverscript.xxx",
  data: myusername,
  cache: false,
  success: function(data){
     $("#resultarea").text(data);
  }
});