How would I hide a form and display thank you content in the same area - drupal 6
Or use $form_state['rebuild'] in the submit handler and check for submitted values in the form builder. That way you can display the form the first time the user hit's the page, and after submission you display your message. This is something like a multistep form, so you could take any of the numerous tutorials for multistep forms in drupal.
Also have look at the official example in form_example_tutorial.inc