Using your own hatchery:
Drag an egg from your Eudemon bag into the hatchery and it will be hatched in an hour.
If you are disconnected during this time, you'll have to rehatch the egg.
Initially you can hatch 3 Eudemons. But you can hatch more by completing the '4th, 5th, and 6th Hatcher quest'.
Using the Eudemon Warehouse
There are 5 Eudemon warehouses. Five eggs can be hatched in each warehouse and it will take 12 hours to hatch the eggs whether or not you are online.
Market: Maisie(310, 452) Free to use.
Neri(313, 452) require a VioletStone.
Cronus: Nancy(281, 416) Free to use.
Elven City:Lucia(195,91) Free to use