Well, I'm glad you asked.
Let's look at Dinosaur babies. They, when they hatched, were developed and could feed by themselves but needed to be warmed like any other baby animal. What animals today do the exact same thing? Well, it's a long list.
- Pheasants
- Chickens
- Guineafowl
- Turkeys
- Ducks (And Mergansers, which are Ducks)
- Geese
- Swans
- Kiwi
- Rhea
- Cassowaries
- Emus
- And finally, the Ostrich
All of these animals show very close similarities to the Dinosaur. Let's look at one very good and very prosperous animal, the Chicken.
The Chicken may not look like much... HOWEVER, the Chicken is in fact the closest living relative to... The Tyrannosaurus Rex.
It does, somewhat make sense. The Chicken originates from Asia (Originally the Red Junglefowl), were Tyrannosaurus Rex fossils have recently been found. Maybe, after the great extinction, a smaller subspecies of Tyrannosaurus had evolved into the clucking little creatures we eat today.
But let's just skip that mumbo jumbo about how Chickens and the most powerful land predator ever, the Tyrannosaurus Rex, are related, let's talk about how this entire thing will play out.
Firstly, we need an embryo. This is pretty simple, as we can get one from a chicken egg. We could VERY CAREFULLY drill a whole into the egg with a tiny sterile microscope and give it all the proteins to create the little dinosaur. By the way, there are proteins that you need to create teeth, extra tail bones, and scales. Oh, and ALL of this needs to be in a very sterile environment. If anything bad like bacteria gets in the egg, then we have to start over until we succeed.
After we have at least 50 of them, which is enough for a stable breeding population, we can monitor aggression and feeding behaviors. We probably will not need to do this, as if we pick a calm quiet breed of animal (Let's say, a Barred Rock Chicken) then we don't need to monitor it as it is just a genetic mutation. They will most likely go for a very high price at the start, but with prolific breeding (Something Chickens are good at doing!) then they could be common.
(I wonder what would happen if we bred them to mostly feed on meat, grow bigger, and have sharp claws... who knows?)
EDIT: I've decided to add this part as it could be interesting to see what animals we could de-evolve into Dinosaurs.
Parrot - Psittacosaurus and other Ceratopsians
Chicken - Something along the lines of a small Raptor
Raptor (Eagles, Hawks, etc) - I can see this one creating controversy as many of these animals are endangered. But, I see it as a large Raptor.
Ratites - Ornithomimids. Kiwis are an exception, as they are endangered and controversy would be created.
Vultures - Oviraptors and Ornitholestes.
Swans, Geese, and Swan Geese - Therizinosaurids. Swans, Geese, and Swan Geese would look incredibly close to Therizinosaurids, some of the only plant-eating Therapods.
Ducks - Spinosaurids
Turkey - Probably a Medium sized Raptor
I won't contribute much at this point except that as a geneticist by training I had to weigh in on this bit... As far as I understand it, all birds share a last common ancestor far more recently than T. rex, i.e. all birds, whether chicken or penguin or emu, are far more closely related to each other than to a Tyrannosaur and they're all equally distant in relationship to that creature. Some might share more or less similarity in posture or bone structure, but that's more a matter of subsequent evolution to fit a certain environment. 
