Just put 2 pokemon of the opposite gender in the day care center and you will get an egg. .
How Do You Get A Egg On Pokemon Emerald?
A old women in larviridge town gives you a egg when you talk to her.
You must go to the lava rich town and talk to an old woman then give you an egg
To trick house near cycling road complete it the dude will give you one
Put a ditto and any shiny pokemon (the ditto can be shiny) in the day care, and wait. It will be very random and may never even happen