Yeah sure bud, this is the best resource that isn't a video I could find.
Unfortunately it is in russian but I was able to translate it and if you do too you should be able to figure it out! If not, I've transcribed the most important bits below:
Water dragon - In the water.
Fire dragon - On fire, or in lava.
Aether dragon - On any tile, over about 300 high, above the clouds, make sure it stays up there while it hatches just to be safe.
Ghost dragon - Total darkness, no lights at all. Might also have to be deep down, close to bedrock. Not sure but maybe dig down to be safe.
Nether dragon - Just the same as the nether dragon as far as looks go as far as I can tell, hatch an egg outside of any of these other conditions.
Oh and as for explaining them goes, I'm no expert so please excuse me if this is wrong. I don't have any real source for this so if someone who knew more could explain that could be great.
I'm not sure the water dragon as any abilities but if there were I'd have to assume faster swim speed / water breathing. The fire dragon I'm pretty sure doesn't take damage from ambient fire or lava like the other dragons do. The Aether dragon is slightly faster than the rest, and the ghost dragon glows in the dark.
Edited by Goatfister, 16 February 2014 - 11:43 PM.