In Noxus, any citizen may rise to power regardless of race, gender, or social standing -- strength is all that matters. It was with committed faith in this ideal that Riven strove to greatness. She showed early potential as a soldier, forcing herself to master the weight of a long sword when she was barely its height. She was ruthless and efficient as a warrior, but her true strength lay in her conviction. She entered battles without any trace of doubt in her mind: no ethical pause, no fear of death. Riven became a leader amongst her peers, poster child of the Noxian spirit. So exceptional was her passion that the High Command recognized her with a black stone rune sword forged and enchanted with Noxian sorcery. The weapon was heavier than a kite shield and nearly as broad -- perfectly suited to her tastes. Soon after, she was deployed to Ionia as part of the Noxian invasion.
What began as war quickly became extermination. Noxian soldiers followed the terrifying Zaunite war machines across fields of death. It wasn't the glorious combat for which Riven trained. She carried out the orders of her superiors, terminating the remnants of a beaten and fractured enemy with extreme prejudice. As the invasion continued, it became clear that the Ionian society would not be reformed, merely eliminated. During one bitter engagement, Riven's unit became surrounded by Ionian forces. They called for support as the enemy closed in around them. What they received instead was a barrage of biochemical terror launched by Singed. Riven watched as around her Ionian and Noxian alike fell victim to an unspeakably gruesome fate. She managed to escape the bombardment, though she could not erase the memory. Counted dead by Noxus, she saw an opportunity to start anew. She shattered her sword -- severing ties with the past -- and wandered in self-imposed exile. Now she seeks atonement and her own way to serve the pure Noxian vision in which she believed.

"There is a place between war and murder in which our demons lurk."
Excerpt from the poem, "Scarlet Shon-Xan"

Riven is a Melee DPS champion that is based all on attack damage (AD).
Riven is one my favourite champions and she is what I'd personally call underestimated.
While being underestimated you have a great chance to pack a great deal of damage on the enemies since they mostly ignore you.

I choose that rune setup for the most balance possible. A focus on a certain thing is easily countered, for example if you go all experience runes you'll level fast, but once you reach level 18 you're runes will be useless. This is not something you have to do, nor is it the "best" for Riven (This is simply how I in person prefer to play her).

The Masteries are based on survival & Attack Damage, since being durable as a melee is very important & essential for a melee. Riven's passive allows her to deal great damage and combined with the masteries you get even greater damage! Keep in mind that this is what I prefer on her, NOT the best

The reason why I chose these items is that I prefer to play Riven as an AD "carry" over being the "off-tank" you normally are. Trinity Force gives a very nice boost to your damage output, since you use abilities alot. The Warmog's Armor is simply for health & survivability, and the Atma's Impaler is to balance the losses of getting Warmog's Armor(no armor or damage).

I get Broken Wings at level 1 to be able to either close in on enemies or get away from enemies, Broken Wings is also the major "stacker"[read at bottom of chapter] for your passive. I get " Ki Burst" level 2 to be able to stun on enemies trying to gank, or if you're trying to gank. At level 3 I get " Valor" to be able to close the distance between enemies as fast as possible, which also gives you a nice shield.
After getting Level 1 on " Broken Wings, Ki Burst and Valor" I max " Ki Burst". The reason why I max Ki Burst is the potential to push and easy harass together with Valor.

Note: What I mean with "stacker is Runic Blade. The passive give a great bonus damage which is greatly combined with Trinity Force. But I think you've figured that much out.

I use Exhaust in purpose of sustaining my disabling combo when ganking, so I use my skill combo then Exhaust after while cooldown resets. Flash is obvious, Escaping and Hunting.

Pros

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Cons

× High Damage output

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× No "real" escape skill

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× Durable with this build

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× Big need of teamwork

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× Good Disables for teamfights

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× Hard time versus ranged nukers (ex. Annie)

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× Fast engage for combat

When it comes to team work, Riven can act as an initiator if given the right team.
Riven has the ability to jump in with Broken Wings followed by a Ki Burst which creates a great opening for your team to follow up with some easy placed skillshots and easy focus.
I always start with activating Blade of the Exile for maximum damage possible, and fire it away after my combo and a few other pokes from my team, which could ultimately lead you 1 kill if team focuses same target.

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If you dont have any tanky items like Warmog's Armor & Atma's Impaler I recommend to join the fight after someone else initiated.

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As for farming Riven is excellent

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At a start I recommend a focus on last hits to avoid pushing and chance for enemy jungler to gank.

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Once you've gotten your " Ki Burst" up to higher levels you can easily farm, Using 2x " Broken Wings" and a " Ki Burst". This combo should kill all the mage creeps on lane.

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As for lane setup I personally prefer being with another stunner or a good ranged champion, over being solo.---
My Personal favourite lane-partner is Leona. Leona and Riven makes a excellent combo for disabling and holding enemies at bay.

This guide provides my own ideal Riven build, I do not claim in any way that this build is for everyone, nor is it the best.

Now go out there and show your foes the Wrath of the Exile!