Well, Jonathan, I can't speak for all of the artists on the list, but I can tell you what has worked for me:
I went to an art college for a bachelor's degree (The Columbus College of Art and Design), with an illustration focus. I took as many courses as I could that would allow me to draw living people first of all, and took as many opportunities as I could to go to the zoo and sketch animals there. These courses and exercises teach you many things about how light and shadow work and about anatomy and how to render textures and so forth. As far as I know, there aren't any readily available courses being taught anywhere that feature live instruction on drawing dinosaurs, though. Ultimately, learning to draw can be very quick, but learning to draw well can take a long time; most artists that I know are constantly learning and improving their drawing and painting skills.
Since non-avian dinosaurs are extinct, it's really essential to being any drawing of a dinosaur with a good study of the skeletal remains of the animal in question. This can be a hit-and-miss affair, though; many museums have mounted skeletons with errors that are not yet corrected; go to the Carnegie Museum in Pittsburgh, for example, and you can see the _T.rex_ in the main dinosaur hall standing upright with something of an incorrect skull shape, but then if you go out to the hallway you can see another _T.rex_ in a more dynamic and (hopefully!) more accurate pose, and the skull with the proper shape. Go to see "Sue" the _T.rex_ and you'll see that her skull is distorted, but if you are able to find "Stan" the _T.rex_ mounted somewhere, you'll see one of the best and least distorted theropod skulls around...and even with Stan's skull, you have some strangeness happening with the teeth, and you'd need to correct for that... Most _Stegosaurus_ mounts that I've seen have the tail dragging on the ground, etc...the point is that museum displays can be great and certainly worth studying, but they aren't necessarily the best to use as reference for drawing dinosaurs...so it certainly pays to check with other reference besides the museum displays.
Warning! Stylistic rant ahead!
Some people have been kind enough over the years to publish some good tips and drawings that can help out the beginning artist; HP Tracey Ford has an excellent How To Draw Dinosaurs series that has been appearing in Prehistoric Times magazine and also available in a 2 book set from HP Ford...HP Gregory S. Paul has much good information about the depiction of dinosaurs in the hard-to-find Predatory Dinosaurs of The World and The Scientific American Book Of Dinosaurs, for example. Gregory Paul has made many good skeletal drawings of dinosaurs, found in various dinosaur publications. These are good tools for learning to draw dinosaurs, but watch out for what I'm going to call the Greg Paul Syndrome; this happens to many artists as they are just getting into dinosaur art. Since HP Paul has made so many excellent skeletal drawings and 'life drawings' of dinosaurs over the years, his work has inspired many young artists, and sometimes it's difficult for these young artist to get past the desire to emulate the artists that inspired them. What I mean is, if you find a few years from now that your _T.rex_ drawings all seem to be depicting a profile of the animal in a full running posture with irregular circular patterning and your peers keep making comments like "wow, that looks very Greg Paul-ish!", then you're in danger of Greg Paul Syndrome. All that this means is that it's OK to emulate your inspiration for a while, but if you want to get serious about it, eventually you have to begin to break away and find your own 'look', your own style. That's not to say you can't ever draw a running _T.rex_ in profile again, of course; just find a way to make it your own. This kind of thing can happen with any artistic inspiration; maybe you're really inspired by James Gurney or John Gurche or someone else; again, it's OK to draw inspiration from other artists; I think every artist does it. I certainly do. But you really just have to make it a point to take that inspiration and find a way to make the art your own.
OK, end of stylistic rant.
As for what I do besides dinosaur art; I'm one of the lucky ones that get to do illustration full-time during my 40 hour-a-week job. I'm an illustrator for the Mayo Clinic's books and website.