Drupal - How can I know which button was clicked?

You must use $form_state->getTriggeringElement().

Best practice is to define a #name attribute for your button, so you can have this value in the triggering_element.

For example:

$form['delete'] = array(
  '#type' => 'submit',
  '#value' => t('Delete'),
  '#name' => 'delete',

In this example: $form_state->getTriggeringElement()['#name'] will return "delete" when called within public function submitForm(&$form, $form_state)

If you don't define this attribute triggering_element will hold the button's #value (the text that user can read), but this is discouraged as other modules may change this value or be changed by the localization).

You may use $form_state['clicked_button'] too, but this is deprecated.

You can read more info at the drupal_build_form function documentation page.

$form_state['clicked_button']['#value'] will tell you which button was clicked on the form.

Compare these values in $form_state I have been doing in Drupal 6 and would be same in Drupal7

if($form_state['values']['ok'] == $form_state]['clicked_button']['#value']){
    //Process if OK is pressed
}else if($form_state['values']['cancel'] == $form_state]['clicked_button']['#value']) {
    //Process if Cancel is pressed