This build is made to make Riven an amazing off tank damage dealer. The difference between the builds is rune and mastery set up to show some different routes you could take. I'm mostly making this an item, rune, and mastery outline since she is still pretty new.

Build 1:

More focuses on early game damage then later balancing out to survivability.

Build 2:

Focuses on starting with more survivability with some damage.

You are always going to want to start off with a dorans blade for that extra boost of health and that early game damage. In build 1, I use it with heart of gold to help my B.F. sword rush and in build 2, I stack 2 of them since I am going with more survivability in the beginning of the game.

Boots:

Are mostly personal preference or depends on enemy team. If you prefer speed like I do, you would go boots of swiftness, but if their team has a lot of cc, it would be best to go mercury treads. In build 2 if they had a lot of auto attackers, like that damned caitlyn, you could go ninja tabi to really get the upper hand on them.