I'm going to stay away from anything other than pure scientific terms and the offer of some web links if you really want detail! If you do, let me know and I'll find a way of posting a link or two to you.

To be honest the general answer is, everything we know is an educated guess, but our best guess is that it was akin to birds.

In some ways it may well depend on the species as well, but what is highly suggestive is that T-Rex and Allosaurus (and therefore likely most of the related species) had a medullary bone, similar to that found in modern birds. Further the bone has also been found in Tenontosaurus, which diverged from the Allosaurus/T-Rex genetic line very early in dinosaur evolution. This is suggestive that the majority of dinosaurs (at least of these lines in evolution) would have worked in the same way.

Birds produce this type of bone tissue around the time of laying viable eggs.

I hope that nothing in the above is NSFW, if it is I apologise, but I've tried to keep it away from the area.

Therefore, this is only my personal opinion.

You opened this discussion with scientific intent, and didn't use any vulgar words, so I think you are safe. The admins may have different ideas, I'm afraid.

As for dinosaur reproduction, I suggest we use birds only to compare anatomy, or mating behaviour with smaller dinosaurs. Larger dinosaurs, such as Triceratops may have the same problems as elephants, so their reproductive tactics and behaviour may be similar. After all, supporting extra few tonnes of love is hard on the bones, lousy pun intended to keep it SFW.