How to find out when next() reaches the end, then go to the first item

Determine the .next() ahead of time by checking its length property.

$('.nextSingle').click( function() {
       // Cache the ancestor
    var $ancestor = $(this).parent().parent().parent();
       // Get the next .newsSingle
    var $next = $ancestor.next('.newsSingle');
       // If there wasn't a next one, go back to the first.
    if( $next.length == 0 ) {
        $next = $ancestor.prevAll('.newsSingle').last();;
    }

    //Get the height of the next element
    var thisHeight = $next.attr('rel');

    //Hide the current element
    $ancestor.animate({
            paddingBottom:'0px',
            top:'48px',
            height: '491px'
        }, 300);

        //Get the next element and slide it in      
    $next.animate({
            top:'539px',
            height: thisHeight,
            paddingBottom:'100px'
        }, 300);
});

By the way, you could replace .parent().parent().parent() with .closest('.newsSingle') (if your markup allows it).

EDIT: I corrected the thisHeight to use the $next element that we referenced.