Drupal 7 forms that modules create can be changed by other modules and even themes with the help of Drupal FAPI hooks system. See Drupal 7 Hooks for a list of Drupal system hooks. The hook that allows to edit the existing forms is
hook_form_alter. See the hook_form_alter() documentation at Drupal API site.
The syntax is
hook_form_alter(&$form, &$form_state, $form_id).
In this hook call, $form is the array of form elements (see Drupal 7 Form API Overview article). $form_state has the keyed array of the state of the form, that can change on form submission or in multi-step forms. And an important parameter is $form_id, which has in it the unique name of the form. Drupal core will cycle through all the registered forms, passing their initial array, state, and unique id to this hook function.