Do you mean the physical act of hatching an egg? Or what will the egg hatch into?
First one: eggs hatch by walking around with them. If you want speedy hatching, get a Pokemon with Flame Body or Magma Armour as its ability, put it in your party along with the egg and it will halve the time the egg needs to hatch.
Second one: The resulting species of Pokemon will always be the same as the female parent; the female parent determines the species, the male parent determines egg moves. However, when you breed a Ditto with something that is not a Ditto, say Rotom, the resulting baby will always be a Rotom. The only way to get a Ditto offspring is to breed 2 Dittos together.