First, you should have a method with a name like serviceActionThing in your module. The form's code can be taken from the example here: https://una.io/wiki/Dev-Forms#example-of-usage. So it will look like this:

function serviceActionThing () {

bx_import('BxDolForm');
$oForm = BxDolForm::getObjectInstance('sample_form_objects', 'sample_form_objects_add'); // get form instance for specified form object and display
if (!$oForm)
    die('"sample_form_objects_add" form object or "sample_form_objects_add" display is not defined');
$oForm->initChecker(); // init form checker witout any data - adding new record
if ($oForm->isSubmittedAndValid())
    echo 'inserted id: ' . $oForm->insert (); // add new record to the database 
return $oForm->getCode(); // display form 

}

And the MySQL code to insert the block which uses this method will be following:

INSERT INTO `sys_pages_blocks`(`object`, `cell_id`, `module`, `title`, `designbox_id`, `visible_for_levels`, `type`, `content`, `deletable`, `copyable`, `order`) VALUES

('bx_persons_home', 1, 'bx_persons', '_[lang key for the title of this block]', 11, 2147483647, 'service', 'a:2:{s:6:"module";s:10:"[name of your module]";s:6:"method";s:13:"action_thing"}', 0, 1, 0);

The highlighted parts relate to the mentioned things. The s:10 means the string length of the name of your module so the defined number may have another value.