Prehistoric animals represent the vast majority of extinct animals. Thru Paleontological exploration, scientists are slowly piecing together evolution from the fist sea dwelling organisms to present day species. There will always be much speculation as to what caused the extinction of the dinosaurs.
A lot of plants and animals existed during the Mesozoic along with the dinosaurs. Some animals were closely related to the dinosaurs, like the pterosaurs , which belong to the Archosaur clade, as do the dinosaurs. Other archosaurs include the crocodilians (crocodiles, alligators, etc.) and the birds, and pterosaurs. (All dinosaurs lived on land; none of them flew or lived in the seas.)
Many well-known animals lived before the dinosaurs did. Trilobites (which were arthropods, as are crabs, insects, and spiders) dominated the seas during the late Cambrian period (540-500 million years ago). Much later, in the late Paleozoic Era, during the Permian period, the Dimetrodons lived. The Dimetrodon is more closely related to us than to the dinosaurs.
Fossils of prehistoric animals
Fossils are not old bones - at least, not always. These ancient traces of life come in a variety of forms. Some are old bones, more or less altered by chemical processes. Others are old turds (coprolites, technically), or "trace fossils" like footprints or impressions of skin, feathers or scales.
Fossilization - the preservation process - requires that the organism - or the footprint or impression - be covered with sediment before it is eaten or washed away. On land, this often happened when the corpse washes into a river and is covered with sediment. Generally, only hard tissue - bones and teeth - survives fossilization, but there were rare cases where some fool got lost in the mountains and ended up in a glacier for long-term storage cold ice.
These are some of the processes that produce fossils:
Permineralization occurs when water-borne minerals deposit around the bone structure.
Petrification happens when minerals replace the bone structure itself. This process can replace the organic molecules one for one and thus can show the bone in microscopic detail.
A natural cast occurs when flowing water removes all the original bone, leaving an impression of its outside.
Since sediment is essential to fossilization, the place to look for fossils is sedimentary rocks, preferably in rocks that we know formed when conditions were hospitable to dinosaurs. These rock formations should also be rapidly eroding (erosion wipes away surface layers of rock to make life easier for dino diggers). Seriously, sediments accumulate rapidly (at least in geologic terms), and after 64+ million years, you've got a tower of rock. Thus dino-hunters have no choice but to look for specimens in gullies, cliffs, and other heavily eroding lands.