Depending on your build, Riven is either a lifesteal bruiser or an assassin. The lifesteal bruiser build looks something like 
, and the assassin build is 
You can mix LW into an assassin build, but if you feel like you want a BT or DD, just finish Rav earlier (early Tiamat is nice if you can combo with it), or replace DD with Youmuu's or grab an EoN in the lifesteal bruiser build if you want more burst.
As a lifesteal bruiser, you wanna play like a high damage diver/splitpusher. You duel pretty well, and can survive for a long time if you lifesteal properly. In a teamfight, you wanna wreak havoc on the back line and then just fight with your lifesteal.
As an assassin, you wanna assassinate. If you splitpush, only duel if you can actually outduel whoever it is you're fighting, because if it's a higher damage tank or juggernaut you probably can't, otherwise just splitpush to push, and leave if someone comes who you can't fight.
Assassinating is looking for someone out of position, flashing onto them, and taking them out. Be sure to get something off that kill - if you aren't in a position to do so, don't burn your flash for it. If you can get the kill without flashing, get it, but don't use it if you won't get a dragon or tower or baron off it.
In a teamfight, if you didn't start it by assassinating, look to flash into hopefully multiple members of the enemy back line, and don't get caught up in the front line. AoE assassination is 100% possible, and is exactly what you're looking to do. If you did start the fight, either with a failed or successful assassination, back off, let your teamfights go in, and don't die. Go back in to deal damage to whoever it's safe to do so against - if your flash is down, that rules out any long ranged carries, so just do some burst against their front line, or throw an R at carries who you're teammates got low.
To do all this, you need to know a few combos. Others help with laning, but only 2 are really crucial. A dueling combo, and an assassination combo.
Fast combo is when you need really high dps and can afford to stay in the same spot for ~2 seconds. Basically what you do is auto, wait for when your auto attack damage happens, and like any other auto attack reset, you hit Q right after. While you're spinning in your Q, you wanna click somewhere on the ground, a move command. This will cancel your Q's animation, and then you want to auto attack and click on your target again right after. Feel free to click a lot. You do that 3 times, for each Q.
My personal favorite, and most effective, assassination combo is the doublecast. You E forward, cast R during E, flash, auto attack. This auto attack will need some explaining - start clicking on them before you actually flash into range - this will input buffer it, and make it go off immediately. Then you cast W and Q at the same time. Then you auto once more, ult, and cast Q right after you press R.
