To Hatch all of the following Ender Dragon, Fire Dragon Water Dragon, Air Dragon and Earth Dragon. For the Ender you need obsidian, you have to make a 3x3x3 box and put the egg in the middle of the box. For Fire its that but with glowstone and the Fire Dragon egg. For water it's with sandstone, Air its just 3x3x3 wool with the Air Dragon, For Earth its a dirt box.

How long it takes

7 ingame days aka 140 minutes

Ownership: To own a dragon all you need to do is break the blocks, you'll know when its done because the blocks will be somewhat different.