Let’s imagine you created a login (frontend module) in contao and you want to output that in your own module. There’s a method called getFrontendModule which accepts the ID of a frontend module:
Assuming the login-module has id 9:
// in your class $this->Template->login = $this->getFrontendModule(9);
and within your template:
<?php echo $this->login; ?>
Simple, eh? Would have saved me days if I would have known this earlier.