Why build Riven like this?
Well this is a build i decided to use to make my late game damage nearly as good as my early game damage, as Riven's damage usually drops off late game I find with most builds. Additionally I also didn't want to build a glass cannon. The final build will have ~ 3000 health, with a fair amount of armour and SOME magic resistance. You will be critting for around 700 damage with approximately 50% crit chance, depending on the amount of armour your opponents have, although you can shred through a nice chunk of 90 armour, plus 10% of what they have left with this build.

Why max Broken Wings first?
Honestly, I prefer maxing Broken Wings first as it gives more overall damage than Ki Burst. Either way, feel free to max Ki Burst first if you prefer a short burst of damage. It all just depends on play style.

Your build suX!1!11one
I'm not forcing you to use it. I'm just showing my play-style.

Pros of Riven:
Great damage through the game!
Very mobile
Very tanky (Due to health from items, aswell as low CD Valor
AMAZING ganker
Hard to get bursted down by AP casters.

Cons of Riven:
Can be countered with mass CC
Can also be countered by Madred's Bloodrazor with fast attacking champions, such as Teemo or Xin Zhao.

Why did I choose these runes?
Greater Mark of Desolation
A must for AD champs.

Greater Quintessence of Desolation
More armour pen, what's not to like?

Greater Seal of Armor
More armour, more survivability. Definitely helps alot early game too.

Greater Glyph of Magic Resist
Magic Resistance, something we definitely need, so we don't get squished in half a second by the enemy AP caster.

I use standard 21/9/0 masteries. I like to go with the extra health for earlier buffiness. This makes it easier for you to gank or just get kills in general without dying, aswell as AD altering masteries for overall damage.

I start off with a Doran's Blade. It gives health, AD and a little bit of lifesteal for that extra bit of sustain early on.

I then go on to buy my first Boots, so you may have a slight speed advantage over the enemy.

One thing were missing now is some CDR, so next I buy a The Brutalizer . It gives some more AD, aswell as armour pen ASWELL 10% CDR, which is always very nice to have, especially this early on in the game.

I then go on to finish my Ionian Boots of Lucidity, which should bring us up to 25% CDR, which means you can spam your abilities more.

So right now, you seem a little squishy, which is why I then get either a Phage or a Giant's Belt, depending on how I'm going. If I am tearing up, I will go for the Phage, as it gives more AD and a little bit of extra health. If I'm not doing so well, or if the other team is doing alot of damage to me, I will go straight for the Giant's Belt.

We will then build your Phage or Giant's Belt into a Frozen Mallet. I build a frozen mallet as it generally ensures your target can't get away once you start attacking with it's constant slow, aswell as to give a great amount of survivability.

Now we should have a nice amount of health, so next I build an Atma's Impaler. This will give you a nice amount of AD from your current health. Once you build this, you will definitely notice a HUGE difference in damage output.

Now we will be upgrading our The Brutalizer into a Youmuu's Ghostblade. This will make you impossible to get away from, aswell as giving you some slight crit chance and a bit of extra damage output. This item is amazing, you CANNOT skip this item. If someone pop's ghost, just use this little item and you are sure to catch up to them.

It's time for some more armour pen, and a nice chunk of AD. Next I get a Black Cleaver, as this point in the game, most enemies will have ATLEAST 80 armour. This item gives you 55 AD which is a very nice amount, but it also gives you 15 armour pen per attack, stacking up to 3 times. This is amazing with broken wings, as you can set up all 3 stacks with Broken Wings auto-attack combo (Which is Broken wings, attack, broken wings, attack, broken wings attack) before finishing them off with Ki Burst and Blade of the Exile's secondary use (You should already have this active at the start, or atleast mid-way through the fight).

If for some reason you get to this point in the game, then my last item is Trinity Force. This item is incredible on Riven and you will notice a HUGE difference in damage output when you get this. Although you will be wasting some stats (Mana, AP, The Slow effect), the Unique passive of doing 150% extra damage after an ability is crazy on Riven.
Why is this item amazing? With all of your CDR, you should be contantly using abilities by now, meaning this will always be proccing. You will be doing insane damage after you get this item.

At level one, you should always start off with a point in Broken Wings as it has much better damage output than Ki Burst and will give you much more mobility for harrassing the opponents. Max this ability first.

Take Ki Burst at level two, and max this second (You can max it first, I just max Broken Wings first as it suits my play style more).

At level four take a point in Valor. This ability is amazing, it allows you to juke enemy abilities such as Morgana's Dark Binding with great ease. Max this last, unless you are getting owned, in which case max this second.

And obviously take Blade of the Exile at levels 6, 11, and 16.

The summoner spells that you choose are up to you, and what your personal preference is. Generally I take Flash and Teleport, as Flash gives me a nice way out and should generally be used on EVERY champion considering it is an overpowered summoner spell. I take teleport so I can recall without losing out on much experience, or get to another lane fast if it needs help.

Other recommended summoner spells to take are:
Exhaust
Ignite
Ghost
Cleanse

Summoner spells I DON'T recommend taking, but still have uses are:
Clairvoyance (Why isn't your support taking it?)
Revive (I guess you could get lucky and this may be useful to save your base from someone pushing while your whole team is dead)
Smite (This isn't a jungling guide.)
Heal (I guess if you need the extra help it could be useful, definitely not too useful late game)

Summoner spells you should NEVER, and I repeat, NEVER, EVER! take as Riven
Clarity (OMGOSH OOM AS RIVEN!)
Surge (Why would you?)
Promote (No, you don't want this. EVER.)

Riven is an extremely fun champion to play, and can be hard to master the right play style required for this amazing champ.