Any enters-the-battlefield abilities of the copied creature will trigger if Vesuvan Shapeshifter is entering the battlefield. Any "As [this creature] enters the battlefield" or "[This creature] enters the battlefield with" abilities of the copied creature will also work. If a Vesuvan Shapeshifter becomes a copy of a creature after it's already on the battlefield, these abilities won't apply as Vesuvan Shapeshifter becomes a copy since it's not entering the battlefield; instead, any "As [this creature] is turned face up" or "When [this creature] is turned face up" abilities will apply.