I've attempted everything will be able to think about. It should not be this difficult. Can someone please show me the entire process of using jQuery with WordPress (particularly jQuery Cycle Wordpress plugin)?

in header.php I've:

<?php
    wp_enqueue_script('jquery.cycle.all.min', '/wp-content/themes/andrewhavens/jquery.cycle.all.min.js', array('jquery'));
    wp_enqueue_script('featured-work-slideshow', '/wp-content/themes/andrewhavens/featured-work-slideshow.js');
    wp_head();
?>

I've submitted individuals two js files to my theme's directory.

In featured-work-slideshow.js I've:

jQuery(document).ready(function($) {
    $('#featured-works').cycle('fade');
});

As well as in my template, I've:

<div id="featured-works">
	<?php query_posts('category_name=featured-work&showposts=5'); ?>
	<?php while (have_posts()) : the_post(); ?>
		<div class="featured-work">
			<div class="featured-work-image-container" style="float:left; width:600px;">
				<?php $image = get_post_meta($post->ID, 'homepage-image', true); ?>
				<img src="<?php echo $image; ?>" width="500" height="300" style="margin-left:30px;">
			</div>
			<p style="float:left; width:300px;">
				<?php the_title(); ?><br />
				<a href="<?php the_permalink() ?>">Read More!</a>
			</p>
		</div>
	<?php endwhile;?>
</div>

What shall we be held doing wrong???

BAAAAH!!! I have figured it. I accidentally didn't remember to specify your path:

<?php
    wp_enqueue_script('jquery.cycle.all.min', '/wp-content/themes/andrewhavens/jquery.cycle.all.min.js', array('jquery'));
    wp_enqueue_script('featured-work-slideshow', '/wp-content/themes/andrewhavens/featured-work-slideshow.js');
    wp_head();
?>

must have been

<?php
   wp_enqueue_script('jquery.cycle.all.min', '/wp-content/themes/andrewhavens/js/jquery.cycle.all.min.js', array('jquery'));
   wp_enqueue_script('featured-work-slideshow', '/wp-content/themes/andrewhavens/js/featured-work-slideshow.js');
   wp_head();
?>

otherwise, it really works all right

Duders… 

throw a get_bloginfo("stylesheet_directory") to create your existence simpler

 <?php wp_enqueue_script('jquery.cycle.all', get_bloginfo("stylesheet_directory") . '/js/jquery.cycle.all.js', array('jquery')); ?>