Welcome to the Planet!
Regarding your question, I think you want to frame it less as "How do I paint them realistically", since no one has ever seen a dinosaur, and more as, "How do I paint it according to the latest fossil evidence and interpretations?"
Stan Winston's dinosaurs in "Jurassic Park" met that standard pretty well, for their time. Michael Crichton researched the most recent finds and interpretations, when he wrote the original novel (which was far better than the movie, by the way). I think of paleontologists like Jack Horner and Robert Bakker, especially, who helped replace the older idea of dinosaurs as big, sluggish lizards with the idea that generally, dinosaurs were warm-blooded and more active. The case for close kinship to modern birds was made more strongly, but the discoveries that suggest that specific species were feathered were still being made and interpreted. Crichton described the baby tyrannosaurs as covered with downy feathers, for example, which they had for insulation and shed as they grew.
But as far as colors go, and how many had feathers or didn't, is still not 100% proven in every single case.
So what you will see online will consist of a lot of artistic license.
Having said that, you can still look to existing examples in nature for inspiration and for guidance. For example, there are animals with leathery skins, which might serve as models for you for large animals like the sauropods, or the ceratopsians. You can decide on the lifestyle your animal led-was T-rex an ambush predator, living in forests? Then what would make sense for an animal like that? Or you can decide that your animal didn't need coloring for survival, so it had color for signaling-to rivals, to mates.
You can decide that since modern birds have this or that feature, it makes senses that animals distantly related to them, earlier in the biological tree, had similar features (that's what Crichton did in much of his descriptions, for example). Birds can see colors, for example, so it makes sense that they use it for a lot of things. Dinosaurs may have had similar vision, and so, maybe they used colors in similar ways. Dilophosaurs had crests-were they brilliantly colored? Or did they support some other structure, and so, looked different? What about ceratopsians? Traditionally, a lot of illustrators depicted them like rhinos or elephants. Were their crests colored by species?
And then, the feathers-which animals had them? There is fossil evidence now for some species, remnants of the support structures for feathers, for example, or imprints in the stone. How much were they like the feathers of today's birds, whose feathers are varied, too? There are flight feathers, feathers that provide insulation, and feathers that don't help with those functions, but help with display and recognition, like a peacock's feathers.
Those are all things to consider, and yet, you still have a lot of room for your own imagination.
As far as searching the web goes, I'm afraid I can't give you any pointers. I run a search on "dinosaurs" and find a lot of illustrations, at least. I do have a similar beef about finding the latest info in print. The last books I bought were Bakker's "Dinosaur Heresies" and Horner's "Compleat T-Rex", and those are now 20 years or more behind us. I don't know of any contemporary paleontologists who have written like Bakker and Horner, for a general audience. There is content on YouTube, and I'm probably showing my age when I talk about looking for books, when someone in his 20s instinctively goes for online content. Having said that, I follow a Facebook page for paleontological artists, though I'll have to get the exact name for you. But if you use Facebook, just search on "dinosaurs" and I'm sure you'll find a lot of content there. Same goes for YouTube. Another website that has some good illustrated content is DeviantArt.com. It's an artists' forum, but there is a good contingent there of people who do illustrations, and models, of dinosaurs and other prehistoric animals. I recommend looking there, too.
As far as my own preferences and ideas go, I think a rex would look cool with stripes like a tiger or spots like a leopard-to help conceal the animal from potential prey (I think Horner makes a better case for his ideas). I have the second-generation Tamiya kit, and I'm leaning towards one of those patterns.
But no one's ever seen one, so, who's to say?
There are some other Planeteers who specialize in prehistoric animals, who will probably have better insights to help you, too.
Prost!
Brad