Excerpt of functions.php for calling a Javascript file in your wordpress theme

functions.php

/////////////////////////////////////////////
// Add custom jQuery plugins and functions //
/////////////////////////////////////////////

 function aaathematic_scripts() { // name the function something unique to your theme
	
	if ( !is_admin() ) { // instruction to only load if it is not the admin area
       wp_enqueue_script('sample_js_file', get_bloginfo('stylesheet_directory') . '/js/aaathematic_scripts.js', array('jquery'), '20100329' );
       // the above line includes the name of the file, where the file is in relation to the stylesheet directory, specifying that you're using jQuery and a version number for your file
		}
		
	}
add_action('init', 'aaathematic_scripts'); // be sure to use the same function name that you did above!

sample_js_file.js

var $j = jQuery.noConflict();

/*
This makes a selector/div fade in.
This works, but in your style.css file, the selector/div has to be set to 'visibility:none'
*/
$j(document).ready(function () {;
    $j('#content').hide()
    $j('#content').fadeIn(2000);


	});