This will help get you started a bit.
You need to prevent the normal form submit by preventing the default event on your button. Otherwise the page will reload due to form submitting.
You also need to send data to server. You can get all the form data using serialize()
$(function(){
$('#submit').click(function(event){
event.preventDefault();
// collect the form data
var data = $(this).closest('form').serialize();
// send the data and load new content
$('#content').load('content/submit.php', data, function(){
// new html now exists can run any code needed here
});
});
});