Cockroaches breath through spiracles which are SMALL openings PRESENT on the sides of their body.
The oxygen rich air enters the body through spiracles to tracheal tubes which is called trachea and then diffuses into body tissues, reaching to each cell.
The carbon dioxide that is released GOES into the tracheal tubes and moves out though the spiracles.
Additional Information-
Earthworms breath through their moistskin.
Frogs breath through gills when they are in water and through LUNGS when they are outside of water.