How to show a custom form in a block?
Create a block with hook_block_info and embed your custom form within a block using hook_block_view. Assuming module's name to be example, this module creates a "My block" with the form. 

FYI, in the below code drupal_render(drupal_get_form('MYMODULE_form')); is the one rendering your form in the block where MYMODULE_form is the form ID.

 &lt;?php
    /**
     * Implements hook_block_info().
     */
    function example_block_info() {
      $blocks = array();

      $blocks['MYBLOCK'] = array(
        'info' =&gt; t('My block'), 
        'cache' =&gt; DRUPAL_NO_CACHE,
      );
      return $blocks;
    }

    /**
     * Implements hook_block_view().
     */
    function example_block_view($delta = '') {
      $block = array();

      switch ($delta) {
        case 'MYBLOCK':
          $block['subject'] = t('My block title');
          $block['content'] = drupal_render(drupal_get_form('MYMODULE_form'));
      }
      return $block;
    }