How to implement “hook”?

https://wphooks.flatearth.org/hooks/category_link/

This “hook” is exactly the function I need, but I have a hard time figuring out how I should use it. I bet it’s really easy, but I want to confirm it before I start doing weird stuff to my dear WP!

so, 1) Should I create that file (from that page) called template-functions-category.php in the plug-in directory or in the wp-includes folder ?

2) How would I implement it on my blog, with
add_filter('category_link')?
I would like it to show on my frontpage listing of articles, does that mean I will have to do something like

<?php
$cat = get_the_category();
$cat = $cat[0];
echo $cat->category_link ;
?>">

to call it?

Any help whatsoever would be MUCH MUCH appreciated!