How do you get an azuril?

To get an azurill, you need to breed a male and female marill while the female is holding the sea incense.
Make sure you have the National Dex

Catch yourself 2 Marills in Mt. Mortar

(Opposite Genders)

Put em in the Daycare, wait a while and, voilà! You got yourself an Azurill Egg.