How do you download games on a school iPad?
Your school iPad is being managed with some sort of Mobile Device Management (MDM) software.  Companies and (especially) schools use it with devices they distribute so they can effectively manage who uses and what gets used on the devices (like iPads) that they deploy throughout the organization.

This MDM software is the "teeth" in your school's Acceptable Use policy (AUP).  If you remember from the beginning of the school year when the devices were distributed, there was something that you and/or your parents signed indicating that you would abide by their rules/regulations for use of the device.  

The MDM software is the technological component to ensure students abide by the policies/rules of the organization.

Unless your school policy changes in someway to allow the loading of unauthorized software, you simply can't.