The fossils are a stone block that has a slightly different texture. They are fairly common. They have various different drops. One of the drops is Bio-Fossil. One of the drops from the Bio_Fossil is a random dinosaur DNA "chip." This chip can be put into a culture vat with some Bio-Fossil as "fuel" and it makes an egg. The egg, when placed in the correct biome, and left to be warm will hatch. The baby dino then needs proper food, and can grow.
Finding the DNA and making an egg doesn't have very good science. There is an option for a DNA syringe. I don't currently have the recipe. :( If I knew how to craft them, you can inject them into a pig, cow or sheep and the sheep will be impregnated with a dinosaur. I like this option much more.
I was busy making the tutorial and the MC World, and didn't get to ride/tame a dinosaur yet, but it has great potential.
As a lesson, I created an NPC and "sold" students an enchanted diamond pick, analyzer, culture vat, dinopedia, night vision potions, torches and chicken stew for one dirt each. This way they could focus on finding the fossils.
-Scott