Where can I find the Clean Permalink Code?

Exactly what do you mean by… “clean” ?

Like instead of the permalinks looking like this:

https://www.website.com/directory/index.php?action=reallylongstring

the code that makes them look like this:

https://www.website.com/directory/index.php/string/

try:

classes.php inside the wp-includes directory

Except for the admin panel I have never seen in any “normal” WP installation URIs like you say you have:
website.com/directory/index.php?action=reallylongstring

Where do you get those?