At this point in science we know for sure that dinosaurs had feathers. We aren’t sure which ones did or did not, we do not know how much of their body was covered, and we have no idea what colours they were. However as more dinosaurs are discovered to be feathered, researchers are uncovering more methods for determining their presence and uncovering those mysteries using the fossils available.
Most recently paleontologists at Brown University (Rhode Island, USA) have found a way to figure out the colouration of a dinosaur using the remaining melanosomes (pigment-producing organs in a cell). They can analyse the structure and shape of the melanosomes using a scanning electron microscope. These microscopes can produce some of the most finely detailed images ranging from 10-times magnification, to around 500,000-times by scanning the item with a focused beam of electrons which produces a scanned image, much like a common photo copier. The researchers can compare the structure of the detected melanosomes with those of birds today to estimate the feather colours. In one of their examples they used this method on the fossils of a bird-like dinosaur called Anchiornis huxleyi (second image), they discovered melanosomes that likely produced a mostly black plumage. Source: The Earth Story