I'm by no means a pro-level player. I'm only sitting at level 23 (and a half), so I probably haven't been playing against the strongest opponents. Don't expect gold here, but I tried to make a good build, and this is the first build I've ever put together without any outside help. Enter at your own risk.

Also, I'm not 100% sure on the S3 changes, and I arguably picked a ****ty time to make a build. Therefore, a lot of the advice will most likely be interchangeable between 3v3s and 5v5s.

Alright, this is my first homemade build, so don't expect anything mind blowing. Currently, this only works on Twisted Treeline, but if memory serves, the items will be going into S3 Summoner's Rift.

Riven's my main, her release was my first spur-of-the-moment League purchase, and when I was invited to a 3v3, I found the Bloodthirster (my previous go-to) was disabled on the new Twisted Treeline, I had to quick think up something on the fly. I found that Lord Van Damme's Pillager is good for CDR and can lead up to plenty of excess gold, and Blade of the Ruined King has both lifesteal and a slow, so I swapped those in for the regular two BTs. I play pretty aggressive, in my opinion, and have given up on the often used Tanky Riven, preferring Lifesteal + AD over HP + AD.

She does have less staying power in teamfights early-game if you jump in there without some assistance, but late game, soloing the opposing team should be pretty doable.

My Picks

I typically stick with exhaust and ignite.
Exhaust lets you ensure your team tons of damage on that one target that's been giving you grief (or preventative measures against said target) and also an acceptable way out of a chase.
Ignite's good for ensuring constant damage against a single target in a teamfight and also a chance of scrapping an escaped enemy. That's not to say other spells aren't acceptable, though.

Secondary Picks

Flash and Ghost are two good spells. Need to chase? They both work good, with Ghost taking a slight priority in extended chases. Flash also works great for dodging annoying skillshots, especially ones with attached debuffs (like Morgana's Q). You can also chase/escape over walls, and that's especially entertaining when the enemy's just about to nab a kill from you.

Other Good Stuff

Heal is good because, well, it's a heal. That extra HP can be great when you need it.
Smite's also a good pick if you're jungling, since that an obvious pick.
If you need it, Teleport can work. Basing often can screw up teamfights, and it's good to get back in the action.

Don't Really Bother

Revive, to me, seems like an excuse to die. Unless you really need it, don't pick it. Playing properly, you shouldn't be dead long enough to have any impact on the game, but if it happens, it happens. Take it only if you absolutely need it.
Surge isn't all that important. Sure, the extra AS on Riven is nice to expend those stacks, but she's more about bursty damage rather than auto attacks. You really don't need it, compared to other spells.
Promote seems cool at first, but chunky minions don't take priority over scrapping champs. If you feel like messing around (not usually a good idea in public games), go for it. Otherwise, keep away.
Regarding Clairvoyance, I have two words: buy wards. The extra gold is much better than having a map clear taking up one of your spell slots.

Don't you even think about touching that.

Clarity is not, under any circumstance, to be picked. Riven doesn't operate on any sort of energy, so grabbing it is a total waste.

I pick Broken Wings first for the mobility, but only once. It's good to have those three hops to get around, since they rely only on cooldown, and they're also relatively useful for exploiting the passive damage boost from Runic Blade. The cooldown stays the same for each level, so one level (when used mainly for traveling) is sufficient for now.

Second is Ki Burst. This is good because it scales 1:1 with your AD, and has a short stun included. When you get in teamfights, Ki Burst helps to stun the entire party (a second of no abilities can make the difference) and do a good chunk of damage. I pick this second and third, then max it out by level 9.

Fourth pick is Valor. Again, this is a 1:1 scale with your AD, so properly stacking your AD items can make for an awesome "getting into/outta heavy fire" shield. This is the second skill I max, putting a second level in 7 and maxing at 13.

Blade of the Exile is pretty straightforward, like every other ult. Take it at levels 6, 11, and 16, because it's just that important. Because Riven's abilities scale so heavily with AD, having an extra AD boost right before a teamfight and also having a skillshot to pick up escapees is a necessity.

I'm just getting started with this skill sequence, really, so it can be altered however you may see fit. Broken Wings scales good with AD as well, but in a chase, it's nice to also have a heavy-damage stun that works with you as a deterrent to chasing. If they have hard hitters who like to launch abilities at the beginning of a fight, focus more on leveling your Valor, it'll save a good chunk of your life.

Riven's all about combos, seeing as she basically has seven skills at her disposal in a fight. Broken Wings has a three shot combo, with a jump/slash, jump/slash, jump/knockback. Ki Burst and Valor are single shot, but Blade of the Exile is a double shot. Working around this, we can get some decent combos. NOTE: If you don't already abuse her passive, you definitely should. It's free extra damage, and it's only timing-reliant.

Getting into a 1v1 fight, I jump in with Q -> auto attack -> Q -> AA -> Q ahead of the champ (to knock back) -> AA -> W -> AA -> E to escape/continue combo. R is situational; if it's a beefy champ or one with an escape, use it. If you think you have a decent shot, don't risk it, just in case other enemies show up.

Getting into a 2 or 3 enemy fight, activate your R and jump in with E -> AA -> Qx2 -> AAx2 -> W -> AA -> Q to scatter -> AA. They shouldn't be spread too far from your Q, so launch in an R blast before that cooldown's finished. Properly built, you should do metric ****tons of damage to the opposing team.

Escaping combo's pretty easy: Stun with W -> E -> Qx3 and repeat as necessary. Obviously, you won't need to stun if nobody's in immediate range, just keep spamming Q and E.

Fighting creeps, go nuts. They won't hurt you too bad. I go E -> W -> Qx3 -> AA until something refreshes. If it's vs. a buff monster (in the case that this build ever works on SR), always throw AAs between your skills.

Recap:
1v1 - Q/AA/Q/AA/Q/AA/W/AA/E
1-3v2-3 - R/E/AA/Q/Q/AA/AA/W/AA/Q/AA/R
Escape - W/E/Q/Q/Q
Creeps - E/W/Q/Q/Q/AAxInfinity

Alright, the important bit. I'll break this down by the key items:

Ninja Tabi

Build these at the start. They take some of the heat off AAs, and it's a nice little chunk of armor. Start with the ingredient items and five hp pots, for maximum laning time before basing.

Lord Van Damm's Pillager

This, in my opinion, is a good starter. You've got your health, your damage, and a good CDR and Armor Pen. Build up the ingredient items, but leave it. If you finish the build, you lose your extra GP10 that can be helpful for your other builds (finish it after your BotRK, though, or at least soon after). And then there's the most important part: it's named after Jean Claude Van Damme.

Blade of the Ruined King

Here's your first lifesteal item, and the reason you don't need to build tanky. The Blade has 4% lifesteal based on current health, so the more health they have, the more health you get. It also has a nice slow+speed boost, which makes chasing a little bit nicer. Start with the Vampiric Scepter when you build this. The little bit of lifesteal can help out in the field, so you can feed off creeps instead of needing to base as often. I put off finishing the Pillager, but not this; finish it ASAP.

Black Cleaver

Time to get mean. Black Cleaver's got itself a passive armor crusher built right in, and that'll help counteract the armor-heavy Riven haters out there. If you have the GP for it, buy the B.F. Sword first. If not (and there's too much to just wait for), settling for the Dagger is fine.

These last two, IMO, are interchangeable based on the situation. I usually build in this order, though:

Sanguine Blade

This was my Bloodthirster replacement, and I was a bit disappointed that it didn't have stacking potential. Either way, it's a good source of both damage and lifesteal (another perfectly fine excuse not to build tanky). Take the Vampiric Scepter first for the lifesteal, unless you have the cash for the B.F. Sword. Make sure you're constantly hitting creeps with this, even if it's not kill-shots. The stacks only remain while it's in use, and you never know when there's a Garen in the bush.

Frozen Mallet

Time to pick up some stragglers. Frozen Mallet is an all-around good weapon; it has an okay chunk of damage, but then it gives you 700 extra HP and applies a 40% move speed slow to anyone you hit. Because this works the way it does, it doesn't necessarily need to be built last, I just do it for victory insurance. You can build it any time after you finish the Pillager, and you should be just fine.

Other acceptable items:

Most AD items can work with Riven. Atma's Impaler is good if you ever decide to build tanky, and so is Maw. Jungle Riven (which works pretty decent) can really benefit from having a Wriggles* with her, so the same applies to the Razors beneath it. Infinity Edge is a good AD item, and if you wanna take a shot at crits, go for it. Youmoo's is great for piercing, as is Last Whisper. If you wanna give any of these a shot, have fun.

*Wriggles isn't in TT, of course, just wishful thinking towards S3 Summoner's Rift. And in that case, Bloodthirster is also an awesome pick, but isn't available on TT.

Riven's got good HP protection, damage output, and mobility, which makes her great for the Treeline. Unlike Summoner's Rift, you don't need to worry about picking a solo lane; sure, if you want, you can, but it's a short enough distance between the two that it doesn't really matter. Spamming your Q and E can get you halfway between the two lanes, so choosing one shouldn't be that hard. Makes it really easy to roam.

The best starting strategy I've seen used is just a three-man bush fight. Get all three of your dudes in a bush (usually the top one by the speed booster or another centrally-located shrubbery) and wait. The enemy will come, and that's the exact moment you need to ruin their day. Jump in with Valor and stun them with your W. This'll throw off whatever they had planned on doing and give plenty of time for your allies to lay down some damage. Hell, you might even W all three in one shot, sometimes they're grouped up close enough. The point of this is getting at least two kills for the team. I've never gotten less out of the gate using this strategy, so give it a shot. You don't always have to be a genius tactician to win, sometimes it just comes down to having the bigger stick.

Onto laning and farming. You're gonna wanna get as much gold as possible, so try to take the top by yourself. I understand that on TT not everyone likes to keep to their lanes (in fact, you could say it's discouraged), so when they leave their lane, unless it's for a teamfight, you can view their creeps as up for grab. If they got a good handful, screw your lane and take theirs. If nobody's taking jungle creeps, take them for yourself; they respond fast enough, nobody needs to complain (unless they need the HP or fall behind from disconnecting, then you should probably share). The build is expensive, and you need all you can get. Turrets are also nice to get, but if you can't get one right away, no big deal. They aren't as important before end-game here as they are on Summoner's Rift, so if you can't get one before you nexus push, that's fine. When you do, though, it's perfectly acceptable to use your ult for massive damage. Cast R, then AA, and spam alternating abilities and AAs on the turret. The abilities won't damage the turret, but they will give you some useful extra damage on it.

And regarding your gold gathering skills: the map's small enough that you can play as the AD carry. Don't worry about letting a ranged champ (or anyone else, for that matter) feed, you need it more than they do. You'll probably carry the team on your own anyways, unless you get another heavy damage champ on your team.

Altar's are gonna be important, on the topic of money. Both get you an extra 4 GP, so having both can effectively get you a Long Sword after 52 creep kills on the bonus gold alone. Might not seem important at first, but take those altars! Riven has that mobility, so if you see an open altar, run for it. It also goes to say, though, that she's not invincible early and mid game. If you see more than one enemy by an altar, forget it. You can always get it later.

Vilemaw, the new boss, should be a constant target from level 12 and up. Once you get your Pillager and BotRK, a three-man fight agains Vilemaw is a viable course of action, and all that extra cooldown reduction is awesome (using your W every six seconds: aww yiss), not to mention the HP regen. At level 16, you should be able to solo him singlehandedly, but make sure you're always on that. He's easy enough to take down, but also easy enough to forget about while farming. If you need to, leave particularly vulnerable enemies for the time being to take it (if you can). Don't let em follow you or know where you're going, though; Vilemaw hits hard. He can easily chunk down your life if you aren't prepared, opening up an easy kill window for the enemy.

On the topic of champ fights: get involved in all of them. Even if you don't plan on taking the kill (again, sharing is caring), at least stop in to say hi. Dashing in to land a W so your ally can finish off a champ ensures that both the champion dies and you get assist gold. Every gold opportunity you get, you take it. And the same with Vilemaw, once you get Pillager and BotRK, you should be fine getting into fights. A lot of the stuff going on is gonna be in the mid jungle, so be prepared to use bushes to your advantage. Nobody wants to see a Riven jump out and pop a massive HP melting stun on them, then scrap em with an R rune blast. Use dem bushes and ambush whenever possible.

You're not a damage-dealing god, though; run if you have to. I gave you an exit strategy in the combos section, so use it. I can't explain how useful her kit is when it comes to getting away, like all the times I've gotten away from an upset Wu Kong with only ~70 HP left.

If at all possible, try to team up with a CC-strong ally for fights. If they can hold the enemy champ for even a few seconds with a stun or fear while you pop off your skills, that'll save you some HP to spam more skills later. It's also good to note that when stunned, your priority is to deal as much damage as possible. Spam all your offensive moves immediately, so you can get them up quicker for when they come out of immobilization. Keep your E until you need it, no point in using it while they're stunned, it can be used as a damage booster or escape mechanism. Sure you'll only get three hits in rather than four or five with your passive boost, but you'll get more damage in overall quicker if they're stunned.

Also important (again), watch those altars! People get gold hungry, and its your job to stop them. You can usually catch them off guard standing on the altar, so jump up, stun, then blast em hard. If you're lucky, you'll get em before they can take the altar.

To sum up TT gameplay: Get involved in everyone's business. Know when a fight's going down so you can wait in nearby bushes, get your R ready to finish fights, and get good at at least stunning the enemy so someone else can finish them off. Assist gold is better than no gold, and you're gonna need all you can get.

Build Riven with a socially acceptable amount of AD (i.e. lots), and throw in a decent chunk of lifesteal to counteract your lack of tons of health, since you won't get any until later parts of the game. I'm really starting to like this build, since my last round I solo'd Blitz, Lee Sin, and Annie, and can solo Vilemaw at level 15 and leave with full health. This can still be categorized as a work in progress, since I'm not as experienced as a lot of other players. Any tips you have for improving the build/playstyle would be greatly appreciated, I wanna make this as good as I possibly can without having to completely rewrite it.

Here are some results I've had. The only two losses I had were because I surrendered after having both teammates disconnect from the match for extended amounts of time.