How to display related posts from this code?

I think you have two options on how to use the functions you’ve found. The first one is to add one of the functions to your single post template file.

pew_related( 
  array(), // add custom parameter key=>value pairs, if needed
  get_the_ID(), 
  '' // not sure what is the purpose of the third parameter 
); 

or

$related_posts = exe_get_related_posts_by_common_terms( get_the_ID(), 3, 'post_tag', 'post' );
if ( $related_posts ) {
  // foreach loop the $related_posts array for desired html output
}

The second option is to hook one of functions to suitable action or filter. For example,

// functions.php
add_filter( 'the_content', function($content){
  if ( ! is_singular( 'post' ) ) {
    return $content;
  }
  ob_start(); // push html output to buffer
  pew_related( 
    array(), // add custom parameter key=>value pairs, if needed
    get_the_ID(), 
    '' // not sure what is the purpose of the third parameter 
  ); 
  $related_html = ob_get_clean(); // get buffer content
  return $related_html ? $content . $related_html : $content; // concat html to post content
} );