You get eggs the same way you get every other egg... by breeding.
You take two Pokemon and put them in the daycare as long as they are in the same egg group, or when bred with a Ditto.* (You cannot breed legendaries)
In your case, take an Eevee (or two) and breed it with a Ditto; you will eventually be able to get an egg in the daycare.
To obtain an Eevee to breed, I think you can get one in the Game Corner.
- 12.22.2011 4:04p