A Dinosaur is a Tetrapod - it has a backbone - so do mammals and fishes.
A Dinosaur is a Reptile - Reptiles are cold blooded, lay eggs and breath air (mammals are warm blooded and produce milk to feed their young, fish don't breath air).
A Dinosaur is a Diapsid - A diapsid has two holes on the sides of the skull called temporal fenestra (openings). Turtles and marine reptiles are anapsids with only one opening.
So, a Dinosaur is a Tetrapod, a Reptile and a Diapsid. But Dinosaurs can be divided further into two groups by the shape of their hip bone: