How to easily create a custom module for Drupal 6?

Let's break this down into a few easy steps.

1. Know where custom modules go, not in /modules but in /sites/all/modules
2. Create a new folder there, e.g., new.
3. Open a text editor and create a file named new.info
4. In new.info add the following lines:
   
   ; $Id
   name = New
   description = A new module for testing
   package = Other
   core = 6.x
5. Create another file named new.module
6. In new.module add the following lines:
   <?php
/**
* Implementation of hook_block().
* Adds a block that has new text.
*/
function new_block($op = 'list', $delta = 0, $edit = array()) {
  switch ($op) {
    case 'list':
      $blocks[0]['info'] = t('New Module');
      return $blocks;
    case 'view':
      $block[0]['subject'] = t('New Module');
      $block[0]['content'] = t('Hi from your custom block and your first new module');
       return $block[$delta];
  }
}
7. Make sure both files are saved and then in Drupal go to Site Building -> Modules. Look under the other category and you should see your new module listed. Just check the box for it and submit.
8. You now have a new module which creates a custom block, you can go to Site Building -> Blocks and you should see your new module block. You can select to enable it and add it your pages. 
9. The possibilities with modules are nearly endless, I recommend you pick up Pro Drupal Development  for more instructions.