There are several ways paleontologists, and paleobiologists, learn about what dinosaurs looked like and how they behaved. Oddly enough a lot of it begins as guess work, then ruled down through trial and error, comparing finds with animals we know of today, until a conclusion is settled on. Even then, with more discoveries some things we thought were true are being challenged and rethought.
Dinosaurs did not leave much evidence of how they lived, they didn't write books, or take pictures of themselves, however what they did leave behind has given us pretty good clues about them.
1. Fossilized Bones
Their actual bones are long gone, replaced by fossils that took the exact shape of the bone when the animal died. In some cases ligaments also became fossils. When scientists excavate the bones (and usually make lighter models of them) they can reassemble them to determine how the creatures looked. There have been several cases of mistaken reconstruction, one of which was the Iguanodon, whose thumbs were at first thought of as nose horns, and who was originally thought to be a quadruped.
Teeth are very telling because they can indicate what a dinosaur ate, sharp teeth indicate it was a meat eater, rounded teeth indicate plant eaters. By looking at fossilized dinosaur teeth and comparing them to todays animals scientists can determine what they may have eaten according to what was alive at the time.
3. Fossilized Skin
Although colors cannot be determined though the use of fossils (fossils are the color of the minerals in the soil), they do indicate the texture of the skin. Recently a fossil was discovered that has given rise to the debate that birds evolved from dinosaurs, because the fossil clearly showed what looked like feather shafts.
4. Eggs, and Nest Sites
Several fossilized nesting sites have been found, some with eggs, and youngsters. This teaches us about how the dinosaurs parented their young. Did they leave them to fend for themselves, like turtles, or did the mother stay to raise them, like chickens? In many cases scientists have come to agree that many species of dinosaur raised their young, not unlike birds of today.
5. Foot Prints
Many individual fossil footprints have been found. These are interesting, but it is the trails that are very telling. They can show what dinosaurs traveled together and which ones traveled alone. They can show if the animals were moving with any speed, and tell a tale, giving us a small, but exciting, window to the past. In a few cases they show how animals hunted. Footprints also hint as to which animals lived in herds and which lived, and hunted, as individuals, or as packs.
In short, coprolite is fossilized dinosaur poop. These give clues to what the dinosaurs ate, some have been found with bones or seeds in it, fossilized of course.
7. Modern Animals
By Studying how the bones of modern animals fit together and relate to how they move and behave, scientists can make better guesses at how these magnificent ancient animals lived, looked like, and behaved.
8. Making Models
When scientists reconstruct the bones of an animal they can also determine how those bones were held together. They can even get a good estimate on how much strength a dinosaur had, or how fast it could run.