Using the Date API module (part of the Date module), you can do something like this...
<?php
$form['payment_expirationDate'] = array(
'#type' => 'date_select',
'#title' => t('Expiration Date:'),
'#date_format' => 'm', OR '#date_format' => 'y',
'#default_value' => $expirationDate,
'#date_year_range' => '-1:+10',
'#required' => TRUE,
'#date_label_position' => 'within'
);
?>
The date_select type will give you select box form elements for your field. And the #date_format array key allows you to use a PHP date format string to control what select boxes appear and what goes inside them.