Instructions
Go to the Daycare Center on Route 117. This is between Mauville and Verdanturf City, at a building with a fence around it and an old man standing close by.
Speak to the receptionist at the desk and select "Yes" when asked if you want any Pokemon raised. Choose any Pokemon you wish to breed.
Select "Yes" on the second dialogue prompt for her to take a second Pokemon. Choose any Pokemon that is the opposite gender of the first one, and not its parent Pokemon. Confirm the selection by choosing "Yes," and go outside.
Speak to the old man next to the fence and make sure he either says, "They don't like each other" or "They appear to care for each other," which is a sign that they will create an egg. If he says "Your Pokemon prefer to play with other Pokemon than with each other," that signifies that the two Pokemon are incompatible.
Let some time pass in the game, then return to the Daycare. Get the egg from the old man, then equip the egg on a Pokemon with the skill Flame Body or Magma Armor. This will cut the hatch time by half.
Walk around until your egg hatches. You have a 1/8,192 chance of hatching a Shiny Pokemon.