How to post value without refresh page with jquery $post?

How to post value without refresh page with jquery $post? Click test1 ,show test1 in div2, click test2,clear div2 and show test2. Thanks.

<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.3.2/jquery.min.js"></script>
<script type="text/javascript">
$.post('index.php',{"id":"div1","name":"post"});
</script>
<div id="div1">
<ul>
<li>
<a href="index.php" name="post">test1</a>
</li>
<li>
<a href="index.php" name="post">test2</a>
</li>
</ul>
</div>
<div id="div2">
this is a <? $_POST["name"]; ?>, just a test.
</div>

HTML:

 

You could make an .ajax() or .post() call to an .php - file, which returns the result (as a div for example). In the .ajax()-function there is an attribute success.
With this attribute you can define a function that is called after the ajax-call has finished:

$.ajax({
    type: "POST",
    url: "submit.php",
    data: submitData,
    dataType: "html",
    success: function(msg){
  }
});

Code (markup):

now you can access the data that you returned in the "submit.php" file over the "msg"-variable in jquery and add it to the div you want to.

But I don't know if there is a way to access the $_POST - values like you tried to do...