How do paleontologists know the exact "cry" each type of dinosaur made?
I remember watching some program that said it was based on the noise produced when blowing through a certain bone. I don't know if this is true or not but if the explanation is similar to it, then does this work for other animals, more specifically mammals? Thanks 
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They don't. We are not sure if all dinosaurs can vocalize. Hardrosaurs are probably vocal because of the hollow structures on their heads that function as resonant chambers, amplifying any sound they may make. Since hardrosaurs are ornithischian (or bird-hipped) dinosaurs, we cannot be sure if theropods and sauropods, which are saurischican (or lizard-hipped) dinosaurs, make noises at all and how they will sound if they do make noises. We do know that the larger an animal. the lower the frequency or pitch of their sounds. It is one reason a human with a large body has a deeper voice than one with a smaller body, and why a bullfrog has a deeper call than a treefrog.
Some scientists are guessing that because the closest living relatives of dinosaurs, namely the birds and the crocs, are both vocal, therefore they believe that dinosaurs are also likely vocal. Whether that is a good guess or not we may never know. Regardless, even animals without vocal cords, such as snakes, can make hissing sounds. Therefore dinosaurs should be able to hiss at the very least.
Simply put, it's about the structure of the nasal cavity and the sound resonance created.
Resonance, as it relates to speech, is the modification of the sound that is generated by the vocal folds as it vibrates (resonates) through the cavities of the vocal tract (pharynx, oral cavity, and nasal cavity). The type and quality of resonance is determined greatly by the function of the velopharyngeal valve. The velopharyngeal valve is open for nasal breathing and remains open for the production of nasal sounds. When oral sounds are produced during speech, the velopharyngeal valve closes, thus directing both sound energy and airflow from the pharynx into the oral cavity. Because airflow and sound travel in a superior direction from the lungs to the oropharynx, the velopharyngeal valve must close completely to prevent speech distortion.
Sorry, but I can't provide a link to this information as it was a pdf and a link is not available.
I think you're refering to Weishampel's reconstruction of the parasaurolophus crest. He built a model of the hollow resonating chamber and blew through it to reproduce the APPROXIMATE sound. We can't be certain of what sound each dinosaur made. It is reasonable to assume, however, that all, or nearly all of them made sounds, not just the hadrosaurs which developed this capability quite far. The closest living relatives of dinosaurs, the crocodilians and birds, make a great dealing of sound. Alligators bellow and hiss. I'd assume that large theropods could hiss and roar, and others made sounds, particularly during the mating season. For extinct mammals we have better extant analogs so little or no need for reconstructions.:)
They don't and nobody knows for sure what sounds they make and they are just assuming or guessing so if a paleontologist looked at one with a long snout they would think the dino made a noise like a elephant.
they dont.