External JavaScript

When I first got my WordPress page up one of the first things I did was attach an external JavaScript file and the JQuery file to go with it. I didn’t have any problems getting the JavaScript to register but now after doing a reset and creating a child theme and all that good stuff, I can’t seem to get it to register it’s existence at all.

Doing research on the matter I keep running into information from this codex:

http://codex.wordpress.org/Function_Reference/wp_enqueue_script

Has something recently been changed that you can’t manually include script tags in the header?

If so, I’m really confused by the codex how to implement my two .js files. Help on the matter would be appreciated!

But I’ve also seen in I think another codex using something like:

<script type="text/javascript" src="<?php echo get_template_directory_uri(); ?>/myScript.js" ></script>

But that doesn’t seem to get me anywhere cept an error:
Uncaught SyntaxError: Unexpected token < error404.000webhost.com/?:1

As well as an error that also appears with the regular script tags that I researched and was told I need to disable the analytics code of my site since I use 000webhost. When I disabled the code it went away, but when I use the script tag above that has the bit of php in it it comes back:

Resource interpreted as Script but transferred with MIME type text/html: "http://error404.000webhost.com/??". hurkybird.com:12
Uncaught SyntaxError: Unexpected token < error404.000webhost.com/?:1

Perhaps these errors are all irrelevant if I just have to use the technique from the codex I linked above?