My trial period has ended and now IDM asks for serial number. How do I get another trial period?

I am afraid that is technically impossible to extend trial period if 30 days have passed. IDM is not free. IDM is free for 30 days only.

You can get your personal Serial Number (product key) after purchasing IDM.

During the installation of trial version of Internet Download Manager (IDM), you have accepted the license that says that you should either uninstall IDM or purchase the full version after the expiration of the trial period.

To get your Serial Number you should purchase IDM.