In a sense, it's much easier to name a new dinosaur than it is to classify it--and the same goes for new genera of pterosaurs and marine reptiles. The classification systems used by paleontologists are based, first and foremost, on anatomy, though behavior and habitat can also come into play if there's any disagreement.
The key concept in the classification of life is the order, the broadest description of a distinctive class of organisms (for example, all primates belong to the same order). Under this order you'll find various suborders and infraorders, as scientists distinguish anatomically between the members of the same order. For example, the order of primates is divided into two suborders, prosimii (prosimians) and anthropoidea (anthropoids), which are themselves divided into various infraorders (platyrhinii, for example, which comprises all the new world monkeys). There's also such a thing as superorders, which are invoked when a regular order is found to be too narrow in scope.
Here's a list of the orders involved in the classification of dinosaurs, pterosaurs and marine reptiles; just click on the appropriate links for more information.
Saurischian, or "lizard-hipped," dinosaurs include all the theropods (two-legged predators like Tyrannosaurus Rex) and sauropods (bulky, four-legged plant eaters like Brachiosaurus).
Ornithischian, or "bird-hipped," dinosaurs include a wide range of herbivorous types, including ceratopsians like Triceratops and hadrosaurs like Shantungosaurus.
Marine reptiles are divided into a baffling array of superorders, orders and suborders, which comprise such famliar types as pliosaurs, plesiosaurs, ichthyosaurs and mosasaurs.
Pterosaurs are comprised of two basic suborders, which can roughly be divided into early, long-tailed rhamphorhynchoids and later, short-tailed (and much bigger) pterodactyloids.