By using hook_form_alter, you can add your own callback functions to any Drupal form.
These functions will be called when Drupal validates the form and when Drupal submits it.

In example below, a module called 'simple_checkout' adds its own handlers to a form called 'ideal_payment_api_issuer_form'. That latter is generated by another module, but we can fill our own tables and run our own validation *in addition to those by the originating module*.