How to get ID of clicked element with jQuery

Your IDs are #1, and cycle just wants a number passed to it. You need to remove the # before calling cycle.

$('a.pagerlink').click(function() { 
    var id = $(this).attr('id');
    $container.cycle(id.replace('#', '')); 
    return false; 
});

Also, IDs shouldn’t contain the # character, it’s invalid (numeric IDs are also invalid). I suggest changing the ID to something like pager_1.

<a href="#" id="pager_1" class="pagerlink" >link</a>

$('a.pagerlink').click(function() { 
    var id = $(this).attr('id');
    $container.cycle(id.replace('pager_', '')); 
    return false; 
});