The first priority in studying dinosaur mating is determining which sex is which. Paleontologists have tried several approaches to this problem, searching for sex differences in size or ornamentation. Frustratingly, though, few species are represented by enough fossils to allow for this sort of study, and no instance of obvious difference between the sexes in the gross anatomy of the skeleton has gone undisputed.
The whole article is a fun read: speculation on how Stegosaurus managed to mate without skewering each other and what early paleontologists thought Tyrannosaurus's tiny arms were for!
And while you're over there you might enjoy Smithsonian magazine's own dinosaur blog.