Any enters-the-battlefield abilities of the copied land will trigger if Vesuva is entering the battlefield. Any "As [this land] enters the battlefield" or "[This land] enters the battlefield with" abilities of the copied land will also work.

If Vesuva somehow enters the battlefield at the same time as another land, Vesuva can't become a copy of that land. You may choose only a land that's already on the battlefield.

Vesuva copies exactly what is printed on the land it's copying and nothing else (unless it's copying a land that's copying something else; see below). It doesn't copy whether a land is tapped or untapped, whether it has any counters on it or Auras attached to it, or any non-copy effects that changed its types, and so on.

If you don't choose a land on the battlefield, Vesuva enters the battlefield untapped as itself, and will not be able to tap for mana.

If the copied land is copying something else, Vesuva uses the copiable values of that land. In most cases, Vesuva will be a copy of whatever that land is copying.