Tectonics is a science that studies tectonic plates. Earth's surface is made of many tectonic plates which move relative to each other. This movement causes earthquakes and can lead to forming a mountain or change in environment.
To determine if Moon has tectonic plates scientists observed Moon's surface for a long time. They were searching for a change in height of a mountins or any changes in surface. If they found this it would mean that Moon has tectonic plates just the Earth does. Only changes they observed were those created by meteorites.
Definitive confirmation that Moon does not have tectonic plates came when people landed on it. Scientific equipment they brought and later the rover that were sent confirmed there are no moonquakes and this led to a conclusion that there are no tectonic plates.