psychic damage

I'm new to this. Can anyone explain how psychic damage works?

It's described as "mind-rending energy" in the rules, but that's about all there is to it. It's usually caused by effects that manipulate a creature's mind or emotions in some way. But it doesn't "work" any differently than any other damage type, as far as the rules are concerned. Is there something specific you wanted to know about it?

Its functionally identical to elemental damage, except its in a more rare grouping type.   The current standing meme explanation is Vicious Mockery and "Emotional damage", or trying to listen to someone saying something so dumb, it actually hurts you.   Some spells specifically describe causing migraines, or a sensation of static interference.  

Outside of that, the one big distinction is things that are incapable of thought or lack INT as a stat (like mundane objects and structures) are inherently immune to psychic damage; and will usually be called out as such.  This does raise a few questions concerning automatons that have purely mechanical "brains" or magically animated objects, because they don't have sentience in the conventional sense, and are typically immune in the stat block. 

Psychic damage is one of the many damage types out there. Usually every damage type works the same. They only gain relevance, when someone has resistance, immunity, or vulnerabilty to a certain damage type.