Adding template with preprocess function

I'll give you a simple example, with all the chaff removed:

<?php

// implementation of hook_menu
function mymodule_menu()
{
  $menu['mypage'] = array
  (
    'page callback' => 'drupal_get_form', //this function is called when example.com/mypage is accessed
    'page arguments' => array('mymodule_mypage'), // this value is passed to drupal_get_form. This means that the function with this name will be executed when accessing example.com/mypage
  );
  return $menu;
}

// callback function for the url example.com/mypage
function mymodule_mypage()
{
  $title = 'title'; // note: text should be wrapped in the t() function. But I'm omitting it for this example
  $contents[] = 'contents 1';
  $contents[] = 'contents 2';
  $contents[] = 'contents 3';
  // we now have string variable containing the title, and an array containing the contents contents. We will now pass these off to the theming function.
  $output = theme('mypage_display', $title, $contents); // we are using the theme function called 'mypage_display', and passing the $title variable and $contents array to it.
  return $output; // this will returns the themed contents to Drupal, which will insert them in the page
}

function mymodule_theme()
{
  return array
  (
    'mypage_display' => array // note: mypage_display is the function we called in our theme() function in mymodule_mypage()
    (
      'arguments' => array('title' => NULL, 'contents' => NULL),
      'template' => 'mymodule_mypage', // Template file without extension. The actual filename will be mymodule_mypage.tpl.php
    ),
  );
}
?>

Now finally, we have mymodule_mypage.tpl.php:

<?php
// Two variables are available in this page:
// * $title, a string which contains the title
// * $contents, ana rray which contains the contents.
?>
<h1><?php print $title; ?></h1>
<?php foreach ($contents as $content): ?>
<p><?php print $content; ?></p>
<?php endforeach; ?>
?>

Hopefully this helps. I didn't test any of it, so there may be syntax bugs, but for the most part it should give you the idea of how it works.