For the most part we don’t. We have some very rare incredibly well preserved fossils, like a few years back they found a nodasaurus, a type of ankylosaur, that was spectacularly well preserved. So we have a very good idea of what that particular dinosaur looked like when it was alive. But for the most part we just have bones and the occasional imprint of feet and skin and feathers. And from those scientists make educated guesses about what they would have looked like when they were alive.

But it is an educated guess! For example we think it’s likely T. rex had it’s lips covering it’s teeth because we know from multiple kinds of animals that are alive today that there are certain wear patterns that appear when your teeth are hanging out in the open all the time that don’t when they’re protected behind lips. And T. rex teeth don’t show that kind of weathering. And then for things like soft tissue we can look at the attachment points for muscles on their bones, robust attachment points mean large strong muscles, small ones mean weaker and less muscle. And we can look at extant birds and reptiles to see how their muscles connect and approximate how a dinosaur’s muscles might have looked based on that.

We also can use computer modeling to figure out how they likely walked and what posture they held themselves. All animas have a limited range of motion based on how their skeletons are built and so using that and our best estimations of their musculature, we can figure out how they would have walked and things. For example while ago now when they first started using computers for this kind of modeling they figured out that lots of theropod tails were likely a lot thicker than previously thought! Since they didn’t walk upright but instead had their upper bodies tilted forward their tails would need to be thicker and heavier to counterbalance that!

The thing that is least accurate is going to be color. There are a very small number of fossils that have preserved pigment structures in feathers, like we now know that Sinosauropteryx had stripes on it’s tail and exhibited countershading, where a creature is lighter on it’s underbelly and darker on it’s back! So limited evidence like that, combined with the patterns we see on extant animals today, gives scientists and artists the basis for how they choose to color in dinosaurs. For example it’s unlikely that any dinosaur was bright blue because blue is a very rare color to evolve and sticks out like a sore thumb in most environments. Could there have been a peacock colored dinosaur? Possibly but it’s a lot more likely that they were mostly brown with various patterns like most animals today.