go to the marsh and just run in mud or surf in water
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You can get azurill in pokemon diamond and pearl by either breeding azumarill (or marill) or capturing it in the safari zone. :]
You can find it in the safari game or if you use surf and swim around in the water but it is not that usual to find it swimming.
After you beat the Pokemon league, go to the Pokemon mansion and keep talking to the man. After a week azurill will appear. :D
Step one: Have a male + female Marill/Azumarill. Step Two: Give one of them (doesn't matter which) a sea insence. Step three: Breed.
Pokemon diamond