Azurill has arrived in Pokémon Sword and Shield, and you can find them in the expansion pack, The Isle of Armor. You can capture them in a specific location on the island, and you won’t need to worry about weather conditions while attempting to obtain it.
You will need to travel to Brawler’s Cave on the Isle of Armor. You can enter it from the Soothing Wetlands, Challenge Road, or the Training Lowlands. Once inside the cave, you should find one bouncing around the first floor of the cavern. They are relatively common all over the cave.
An excellent way to scour all of Brawler’s Cave from top to bottom is to start at the Training Lowlands or the Challenge Road entrance and follow the entire path forward. Following this strict path gives you a direct sight over all of the Pokémon wandering around the cave, increasing the chances for you to locate Azurill during your travels.
Azurill is a Normal and Fairy-type Pokémon, capable of evolving into Marill, and then its final evolution is Azurmill. If you want to evolve it, you need to increase your friendship with it, which you can do by having it in your party during Pokémon battles or by feeding it curry while at camp.