What your asking for has the basic functionality of a plugin, so saying you don’t want to use a plugin doesn’t make much sense.
If you do for some reason want to write your own , using any jquery or JavaScript is relatively straightforward, you enqueue the script where you want it, then wrap whatever data your using in the javascript tags ( usually a div class or id ). This is a very basic example.
http://codex.wordpress.org/Function_Reference/wp_enqueue_script
wp_register_script( 'jquery_cycle_name','http://path-to-your-cycle.js');
wp_enqueue_script( 'jquery_cycle_name' );
The javascript:
jQuery(document).ready(function($) {
$('#featured-works').cycle('fade');
});
Your template or whatever you wrap your info in, typically you want this in a loop to go through several images/posts or content.
<div class="featured-work"> images, etc, go here</div>