I wouldn't say I'm the best Riven player but to this point I'm yet to lose a game or go negative and not carry my team on my shoulders. She can be played many different ways, however I prefer her solo top, tanky dps. She dishes out a lot of damage consistently throughout the game. With this guide, it will give you a better insight on the items and runes I use to succeed, however items won't make you a better Riven player, you need to practice. You can't assume that this build is going to all of a sudden make you carry, it's up to you as the player as well.

Pros

mobile
heavy damage throughout the game
cc
good ult

Cons

can be squishy
need to be aggressive to succeed
with all this free week riven **** and players QQ'ing left right and center, she might have a nerf incoming

See above.
These runes are ideal for laning, they're also the ones I use for jungling as well. At lv 1 you can almost Q combo once with 3 AA inbetween and get first blood.

See above.
Pretty standard melee DPS. 21/9/0.

I go with ignite and ghost, never found a problem with this, I found I don't need exhaust due to a low cd pop up and stun.

My maxing order is as follows, R > W > Q > E

> > >

I max W first for the short cd and more damage on the stun. Most people max E next, however I like maxing Q next, I play very aggressively and often get fed really really fast when maxing these 2 offensive abilities first.

I always start with a Doran's Blade on Riven, it gives good early stats.

Then on my first trip back, I try to grab another Doran's Blade, lv 1 Boots and possibly a ward/hp pots depending on if you got first blood or not. My build now looks something like this:
sight ward
If you have this, you're doing really well.

I then get a Pickaxe and try to finish off my Mercury Treads, I not, I grab extra wards/hp pots. Ideally you'll now have this:
sight ward

Now I finish off my Last Whisper which gives you insane damage, then, depending on the game, start my GA or Bloodthirster. My final build looks like this:


Of course, your build is subject to change, however this is what I usually do and I carry every game. Instead of starting with Doran's, you can skip those all together and get Wriggles Lantern instead, ultimately up to you. I find I'm pretty tanky with only a GA and do insane damage with these items. This build is very cheap, 475+475+1200+2290+3000+2600=10040, plus the cost of wards/pots. 10k should be relatively easy to make in any game. If the game goes longer you obviously get more gold, and should sell your Doran's Blades. These 2 extra item slots can be filled with anything you want really, here's a list of what items I like and why.

If you don't like Doran's Blades, you can get this instead, free 3 min ward, lifesteal, pretty good item. You could also get this on top of Doran's Blades if you wish, just gives more lifesteal.

Lots of hp, built in slow, makes it harder for an opponent to kill you as well as run away from you. Probably the next/5th item I'd get on Riven.

If you're "feeling it" and just aren't getting focused, get this and you'll just wreck your opponents face.

Good item, nice cdr and more armor pen. Not a bad choice, I don't buy it A)I have quite a bit of cdr from runes and masteries and B)I always forget to use the activate, making it pointless.

All the other guides suggest this, I personally don't think that it's necessary, it adds another 5355g to your build and doesn't help her that much. You can build this combo if you like, I suggest not building it as your "core" build but if the game keeps dragging on after you're finished your "core" build, you'd get it as your 5th and 6th items. I personally think a combo would do more justice and be more beneficial to you.

Crazy expensive item, maybe as a 6th item if you're making gold fairly fast or you're "feeling it". The proc makes you hit hard.

Now if you're in need of defensive items (I'm usually not interested in this because I personally don't think it's needed) get these:

If other team has a lot of ad.

raduin's omen Same as above, this give the extra slow and hp, only get if you remember to activate the ability otherwise it's not worth it.

If they have insane CC.

If they're all ap.

Early Game
Since you'll be solo top, your most likely opponent will be a melee fighter as well, which is good for you, as they will have to get right next to creeps/you while they're last hitting. If it's not a melee character, it'll be a little tougher, especially if you can kite you well. In lane, you want to last hit as much as possible while picking your opportunities to harass. For instance, I harass starting as early as possible, if you're both in close last hitting, I quickly attack with a Q combo, Q AA Q AA Q AA, if possible. This either gets them pretty low so they have to pot up, makes then B, makes them use a Summoner Spell, or makes then hug, losing exp. At lv 2 you now have a stun, and should be able to use the same tactics to get first blood. This works because they don't expect you to deal so much dmg at lv 1, so now with the hp advantage in your favor you're free to last hit while they're standing back. Once you get lv 2, you should use Q and go at them if they get remotely close to the minions. Q combined with W at lv 2 should get you first blood with the help of ignite if needed. Your laning game should continue in the same way, by being aggressive and going right at your opponent with your Q W and now E.

Mid Game
You shouldn't be too worried with pushing the lane to far, although they have a jungler, you're escape mechanisms are probably one of the best in the game. While pushing, you should be able to steal your opponents jungle, then when your opponent re pushes his lane back past the middle, you should be able to easily gank your own lane for a kill.

Late Game
You should be pretty fed/farmed, when teamfights break out, make sure you ult before you go in, as there is a delay to cast it. You'll be fine charging in, assuming you have part of if not a GA, unless there is a lot of cc, just be careful when you jump in, like any champ. ie. Don't jump an amumu who hasnt ulted yet... stupid stupid.

To make sure people read the whole thing :P I'll put this tip here.

All the other guide as your main Q/W combo is Q Q W Q, however, the best way to make sure you win a duel/teamfight, Q W Q Q. This is better because, after using Q, the cd duration automatically starts, meaning it'll end at the same time if you go QQQ really fast or Q Q Q. By using W after the first Q, it spreads out your pop up and stun. Also, by using it earlier in the battle, you will be able to get it off more often, and it being a stun, is very valuable. Your full combo in a 1v1 situation should be something as follows:
R Q W Q Q E W R


Good luck, hope this guide wasn't too wordy. Let me know how I can improve, feedback helps.