Simple and addictive! Extermination is a single-player 2D shooter/puzzle game. Kill the foes before they can kill you. It's as simple as that.
WASD moves and use the mouse to aim and fire. As you kill enemies, you earn gold. Use that gold to unlock new weapons and cosmetics.
There's really no penalty for dying, so it's fine to try out different strategies.
Also, if you play your cards right, you can get enemies to kill each other in the crossfire. And keep an eye on the visible enemy reload. That's a great way of knowing when to pop out of cover and shoot.