Playing Multiple Lands in One Turn
Cards don't "add land to your mana pool." They add mana to your mana pool. The little symbols in card text and casting costs represent mana, which you get from tapping your lands (or from other cards like Elvish Mystic, Darksteel Ingot, and Seething Song), not the lands themselves.

New Benalia's ability, "{T}: Add {W} to your mana pool," is actually the same as the ability of a basic Plains card.

From the Comprehensive Rules:


  305.6. The basic land types are Plains, Island, Swamp, Mountain, and Forest. If an object uses the
  words “basic land type,” it’s referring to one of these subtypes. A land with a basic land type has
  the intrinsic ability “{T}: Add [mana symbol] to your mana pool,” even if the text box doesn’t
  actually contain that text or the object has no text box. For Plains, [mana symbol] is {W}; for
  Islands, {U}; for Swamps, {B}; for Mountains, {R}; and for Forests, {G}.


If you have New Benalia and a Plains on the battlefield, you can tap both to make two white mana (like the casting cost for a Precinct Captain), just like if you had two Plains.

Cards that actually put more land into play say things like "Search your library for a basic land card and put that card onto the battlefield tapped" or "You may play an additional land this turn" (e.g. Evolving Wilds and Explore).