Starting in the early 1800's, people began to notice the fossils of extinct animals for what they were, extinct animals. Originally it was assumed that God would never let one of his creations ever go extinct, so these remains that were being discovered must be the remains of something not known in that region. However, as time passed people were realizing that the bones they were finding belonged to nothing that was alive today and therefore must be extinct.
This trend of identifying unknown, extinct animals really kicked off in the 1820's with the discovery and naming of several aquatic animals like the Plesiosaurus (1821) and the Mosasaurus (1822). However, being aquatic animals there was always a possibility that they could still be around, just somewhere off in the deeps of the oceans. This changed as the first extinct land animals started to be identified. In 1824, William Buckland described and named the first known dinosaur species, however the term "Dinosaur" didn't exist yet. The bones, which were far from a complete skeleton, were discovered in Stonefield, England. Even though Buckland realized that he likely knew he had the bits and pieces of several individuals, he knew he had enough of the animal to determine that this is something the world had never seen before.
Buckland described and named his bits of bones in a paper entitled "Notice on the Megalosaurus or Great Fossil Lizard of Stonesfield". His description included images of the lower jaw from multiple angles, some teeth, some vertebrae still attached, or at least adjacent to each other when found, some ribs, pelvis pieces, scapula pieces, a femur, a fibula, and a metatarsal (some of the bones which were misidentified).
Buckland references several people who are, or will be, influential in paleontology in the coming years including Cuvier and Gideon Mantell. Mantell will later come out with descriptions of his own dinosaur the following year and it was this discovery which prompted Buckland to publish Megalosaurus as quickly as he could Based on the size of the bones presented, Cuvier would have estimated the animal to be 40 feet in length and weigh as much as an elephant seven feet high. Buckland seemed hesitant to place those exact dimensions on this animal but he did accede that it had to have been larger than any currently living animal. There was also another set of bones assumed to be from the same species that Buckland was describing which was significantly larger than his primary specimen.
"...the beast in question would have equaled in height our largest elephants, and in length fallen but little short of the largest whales; but as the longitudinal growth of animals is not in so high a ratio, after making some deduction, we may calculate the length of this reptile from Cuckfield at from sixty to seventy feet. In consideration therefore of the enormous magnitude which this saurian attains, I have ventured, in concurrence with my friend and fellow-labourer, the Rev. W. Conybeare, to assign to it the name of Megalosaurus."
Not knowing anything about the animal itself, Buckland also makes a rather interesting assumption about the ecology of Megalosaurus:
"The megalosaurus itself was probably an amphibious animal, and we might therefore expect (as is actually the case) to find it associated with the remains of other amphibia..."
The reference to Megalosaurus being amphibious was because it was discovered in the same deposit as crocodile, turtle, and plesiosaur remains. Buckland however does not attempt to provide a reconstruction of the animal, a common practice in today's scientific world. He describes the animal in both size, as listed above, and as quadrupedal, but doesn't really give any other description by which someone could recreate the giant beast. It wasn't until the 1850's when the world would see a recreation of Megalosaurus in the Crystal Palace exhibits by Benjamin Waterhouse.
Buckland, W., 1824, XXI.—Notice on the Megalosaurus or great Fossil Lizard of Stonesfield: Transactions of the Geological Society of London, v. S2-1, p. 390-396.