Although dinosaur age was the Mesozoic era which covers Triassic, Jurassic and Cretaceous periods, dinsaurs didn't actually start evolving before towards the end of the Triassic period.
During the Triassic, the world's continents were still all joined in the supercontinent Pangaea. That means there were no water barriers and all the dinosaurs could roam the whole area. The remains of triassic dinosaurs that we find today, are therefore similar on all continents. The dinosaur evolution was in its beginning and although there were many different species of dinosaurs, they were not nearly as numerous as those from Jurassic and Cretaceous periods.
Some of the earliest Triassic dinosaurs were Placodonts - swimming reptiles like Paraplacodus, Placodus, Cyamodus and Henodus, which appeared in mid-Triassic and became extinct in the end of Triassic.
Larger water creatures included Ichthyosaurs and Nothosaurs. Icthyosaurs were fish-lizards which are mostly known from Jurassic period, but there are many early shapes of them in Triassic. Many were eel- and whale-shaped, before their classic dolphin-shape became common.
Nothosaurs are the early ancestors of plesiosaurs - the dinosaurs' world's "seals and sea lions". Nothosaurs were not as well adapted to the water as were plesiosaurs, but they were the most abundant fish-catchers of the time.
Pterosaurs, the first flying dinosaurs, evolved in late Triassic. These included Sharovipteryx, Eudimorphodon, Peteinosaurus, Prenodactylus and others.
Carnivorous Theropods such as Eoraptor, Herrerasaurus, Staurikosaurus and Chindesaurus are believed to be the earliest land dinosaurs. Other early threopods included Aliwalia, Shuvosaurus, Gojirasaurus, Liliensternus, and Coelophysids such as Procompsoghnatus, Camposaurus, Coelophysis and Eucoelophysis. Coelophysids were the most widespread meat eaters in late Triassic. Carnivorous dinosaurs developed a fast-moving life style - light slim bodies, powerful hind legs, sharp teeth and claws, and they moved on two legs.
The plant eaters on the other hand developed long necks to reach the food up the trees, long tails (sometimes with a whip in the end, or other armours); and massive bodies so heavy that most of them had to walk on four legs.
Primitive Sauropodomorphs such as Saturnalia, Thecodontosaurus, Efraasia and Sellosaurus were the first plant-eating dinosaurs. True Prosauropods such as Euskelosaurus, Blikanasaurus and Plateosaurus were the main plant-eaters of late triassic times. Other Prosauropods included Lessemsaurus, Riojasaurus, Camelotia and Melanorosaurus.
At the end of Triassic period, a totally new group of dinosaurs evolved - the bird-hipped dinosaurs, (as opposed to the old lizard-hipped dinosaurs above), aka Ornithischians. The most common Ornithischians were Ornithopods, but the group also included the spectacular armoured dinosaurs. The first Ornithischians, which evolved during the Triassic, were Pisanosaurus, Technosaurus, Antetonitrus and Isanosaurus.
NOTE: This website is written in British English, which is the English we use in Australia. You will find words like "traveller", "harbour" and "realise", and they are all correct in the language used in Australia.