You can use event.preventDefault()
$('.button').click(function( event )
{
event.preventDefault(); // default action of the event will not be triggered.
$('.buttonselected').removeClass('buttonselected');
$(this).toggleClass('buttonselected');
});
EDIT:
If you want to load your frontpage (as in your link) and give it a "buttonselected" class than you need to use PHP.
Something like this
if( isset($_POST['page']) ){
$selectedPage = $_POST['page'];
}
View
<a class="button <?php echo ($selectedPage=='frontpage')?' buttonselected':'' ?>" href="?page=frontpage"> HOME </a>