How did dinosaurs get discovered?

There are two strategies, which are worked together. First, go to some area where the exposed rocks are the proper age for dinosaur fossils. Second, look around to see if any of them are "weathering out" of the matrix.

Mineralized bones and other hard parts tend to be a little bit more resistent that the surrounding rock, so as wind and water remove rock, sometimes the bones poke out. Of course, if nobody notices them and digs them out, they eventually weather away as well and we never know they were there.

Some places are particularly likely depositories, such as areas that WERE the terminus of streams because not only might bones have been washed down to them, but the slow-moving water there would have allowed fine particles of clay to settle over them -- just the stuff to make fossils in a few million years.

In any case, the skill of a paleontologist includes 1) patience in shifting, screening, washing and sorting little bits that might be bones and 2) experience in recognizing the things that are. Most fossil bones are little broken bits; it's only once in a great while that a huge solid thighbone or skull weathers out.