If a copied creature is copying something else, Vesuvan Shapeshifter uses the copiable values of that creature. In most cases, Vesuvan Shapeshifter will copy whatever that creature is copying.

Vesuvan Shapeshifter copies exactly what is printed on the creature it's copying and nothing else (unless it's copying a creature that's copying something else or that's a token; see below). It doesn't copy whether a creature is tapped or untapped, whether it has any counters on it or Auras and/or Equipment attached to it, or any non-copy effects that changed its power, toughness, types, color, and so on. Most notably, if it copies a creature that's not normally a creature, it won't be a creature.

If something copies Vesuvan Shapeshifter, the new copy will also have the triggered ability to turn it face down. However, once face-down, it won't have Vesuvan Shapeshifter's morph ability, so it can't be turned face up unless whatever it's copying also has a morph ability.

If a copied creature has {X} in its mana cost, X is 0.

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.

If a copied creature is a token that isn't a copy of something else, Vesuvan Shapeshifter copies the original characteristics of that token as stated by the effect that created it. Vesuvan Shapeshifter isn't a token in this case.