For a Pokéner to catch a Marill to evolve into an Azumarill,search in either the Safari Zone or Mt. Mortar. The Safari Zone is easier. Marill appear at night in a certain area.
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In HeartGold and SoulSilver, she does not battle you - which might be one of the reasons why she doesn't have a starter pokemon. Instead, she has a Marill.
You can catch Lombre in Pokemon HeartGold in the Safari Zone at a waterside area once you receive the National Pokedex.
wait for Mary to tell you where marill is on the game
Find and then catch
You can't catch it. It's a starter pokemon.