Hi i would start by adding a id to the form. and then either go with a onclick on the button element, or just define a click-event-handler for the button.
<form id="my_form">
Name:<input type='text' name='name'>
E-mail:<input type='text' name='email'>
Gender:<select name='gender'>
<option value='male'>male</option>
<option value='female'>female</option>
</select>
Message:<textarea name='about'></textarea>
<input type="button" value="Send" onclick="sendForm()"/>
</form>
Then the jquery/ajax/js part.
function sendForm(){
$.ajax({
type: "POST",
url: "PAGE2.php",
data: jQuery("#my_form").serialize(),
cache: false,
success: function(data){
/* alert(data); if json obj. alert(JSON.stringify(data));*/
}
});
}