Riven is a very good melee fighter, who scales very well with AD. Riven can perform a variety of rolls on a team, but I usually use her as a strict DPS Champ, trying to dish out as much damage to multiple targets as possible, and finishing off anyone attempting to escape from a fight. Riven can also be made more durable for better survival, or she can be turned into an assassin, dealing large amounts of damage to one target, but I find that this build is the most consistent.

Here is some irrelevant stuff:

Pros:
+ Riven scales with AD very well.
+ Riven's ultimate has long range, and is on a very short CD.
+ Riven's farm is very strong because of her mobility, and multi-target damage.
+ Riven is a strong Pusher.
+ Riven is currently underestimated.
+ Riven has TWO Disables, and what are effectively four Movement Abilities.
+ No Mana, YAY!

Cons:
- Riven is kind of Squishy.
- Riven's base defenses are low.
- Riven's base damage is low unless built correctly.
- Broken Wings HATES you, and will never go where you want it.
- Riven must Auto Attack between skill uses to use her full potential.

When playing Riven I usually take a lane with a support character, or solo top. I don't recommend using Riven in mid, or as a jungler. I also don't recommend putting Riven in-lane with another creep-killing champ, as Riven is HEAVILY dependent on last-hitting to get her build going, so she can start putting out stupid good damage. (My favorite lane partner is Taric, because he gives Riven AD, and I'm addicted to AD.)

When Harassing, I usually dash in with Valor, stun with Ki Burst, and hit them, before slashing away with Broken Wings. I retreat with broken wings, so that on my way back, I can walk through the creeps and pick up some last hits, as I really don't want to miss any of them.

Riven's mobility lets her get a large number of last hits, if you see a creep around 25% health, you can use Broken Wings or Valor to dash in, empower her next Auto Attack, and kill it almost 100% of the time. I usually get to about 75 creeps by 12 minutes with minimal effort.

Skill Rundown:
[Passive] - Runic Blade: This is by far Riven's most complex ability. Every time Riven uses a skill, she charges her next Auto Attack to deal extra damage, plus her bonus physical damage. Used correctly , this is the skill that makes Riven what she is.
(This is also the main reason I take AD runes over armor pen.)

[Q] - Broken Wings: This is Riven's main Damage-Dealing skill. When activated, Riven dashes forward a short distance, and swings her blade, dealing damage to all monsters and champions in front of her. This can be activated up to three times in succession, the third time slamming the ground, and knocking all enemies near the point of impact away.
(This is the other reason)

[W] - Ki Burst: This is Riven's second disable. When activated, Ki Burst deals damage in a radius, and stuns all targets hit for a (very) short time. This can be useful in many situations, and can also aid you in landing empowered Auto Attacks on enemies.

[E] - Valor: This is Riven's second Movement Ability, as well as her defensive ability. When activated, Riven dashes forward and gains a Shield (That scales with bouns AD). This ability can be used to block incoming Turret hits, as well as any unwanted cheap shots. It is also good for escaping skills like Swain's Nevermove, and Viegar's Event Horizon.

[R] - Blade of the Exile: This is Riven's ultimate, upon activation, Riven gains bonus AD and Range on all of her attacks, this also enables the use of Wind Slash.

[Secondary R] - Wind Slash: This is Riven's most powerful attack, and by far most deadly skill. Once Riven has used Blade of the Exile, she can activate Wind Slash at any time during it's duration. Riven shoots three projectiles in a cone in front of her, dealing damage based on her AD and the amount of health an opponent is missing. Wind Slash is very good when used on multiple targets, and when attempting to pick up kills. Using Wind Slash does NOT end the duration of Blade of the Exile, so you will still have your bonus range and damage even after using it.

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At the beginning of the game, you want to take a point in Broken Wings, this gives you a small cc, mobility, and a lot of damage. You will want to put your second point into Valor, as it aids in sustain while harassing, and gives you more mobility. You should take Ki Burst with your third point, and then max Broken Wings from there. After you max Broken Wings, you should put points in what skill would aid you more at the time. If you need more damage for farming, put points in Ki Burst, if you need more sustain, put points in Valor. I usually just alternate the two, and keep them Relatively even.

When fighting an opponent 1 vs 1, you should dash in with Valor, and pop your ultimate, then land an Auto Attack (AA), Broken Wings (1), AA, Ki Burst, AA, Broken Wings (2), AA, then use your final charge of Broken Wings to move past the enemy, knocking them backwards from their escape, and land two Auto Attacks. If they are STILL alive, you should be able to pick up the kill with Wind Slash, as it deals damage based on their missing health.

When fighting in a group, it may be better to leave out some auto attacks, in order to keep a majority of the group in-air, or stunned with Broken Wings and Ki Burst respectively. Try to land Wind Slash late in the fight, but on as many opponents as possible, as it will greatly reduce their health if they are already low.

Riven is a strong Pusher, she can clear a wave of minions in one Q-Q-Q-W Combo, and her ultimate is on such a short CD, that you can use it to down a tower in your lane very quickly if given the opportunity. At around 22 minutes, it can take as few as 13 seconds to down a tower alone, making it dangerous lo leave Riven unoccupied with killing your entire team.

For runes, I take flat AD Marks, Seals, and Quintessences, aiding in Riven's last hitting, and early game harassment. Riven's scaling is so good, that taking these makes her deal out a lot of punishment, particularly with Broken Wings, and her passive-enhanced auto attacks (Valor also scales off of AD, giving you more survivability when dashing in). If you can't pause and Auto Attack successfully in between casts of Broken Wings, you may want to take Armor Pen Runes until you can do so easily.

I also take Magic Resist per-level glyphs, as Riven's base defenses are very low.

For masteries we go 21 - 0 - 9. Riven is more of a burst-oriented champion, so I take four points in Sorcery in an attempt to reduce her CD's, but you may find that you prefer Lethality if you plan on adding in some Crit, either one is acceptable. Sunder and Offense Mastery are Key in boosting Riven's damage, and aiding in last hitting. Riven needs to be able to rush in and last hit, and if there is an opportunity, you don't want to loose it because the creep's health ends up at 1 or 2. Brute Force and Havoc, once again helping her damage output, I don't have much to say there.

For items, I pick up my shoes, and three health potions to start off, you could also take a long-sword and one potion, as Riven still scales very well, but I choose boots to make sure nobody gets away from me. On my first trip back, I get a Pickaxe, unless I am doing exceptionally well, then I would pick up a BF Sword. The Pickaxe should later be built into a Lash Whisper, to make up for the lack of Armor Pen. The BF Sword can be built into either a Bloodthirster, or a Black Cleaver, Riven's core items. I usually get the Bloodthirster (Giving Riven lots of sustain) first, because of Riven's AD. After you get your first core item, be sure to pick up your Boots of Swiftness, wouldn't want to let any of them bad guys get away. Once you pick up both your core items, you will be tearing through people in fights. At this point, either the game is over, or it is a good idea to build based on what you see yourself needing to deal with any dangerous champs. If I want to get more damage and stay alive for late game, I get a Frozen Malet, Atma's, or Warmog's.

Be sure to pick up at least the lizard buff at some point, if not golem, as Riven likes buffs.

For summoner skills I take Exhaust and Ignite. Exhaust is essential, but I SHOULD probably take Flash instead of Ignite, at the moment I am trying to keep myself from doing stupid things just because I know my flash is off CD. Exhaust helps with chasing opponents once they decide your damage is too high for them, and shutting down mean Auto-Attacking melee champs. I take Ignite to try to secure more kills, but Teleport, Flash, or Ghost are fine here too.

I hope my guide helped you in playing/building/mastering the use of Riven. Pleas rate up... or Thumbs up, or whatever if you liked it, and don't refrain from leaving a comment and calling me an idiot or something, because I probably am. If you could help me put more images in, that would be appreciated. Also, yell at me for any typos, because I tend to hide them in EVERYTHING I write.

If you have any problems, or need me to update the guide, Email me.

I hope do be adding a video for some of the things here to better illustrate skill-usage etc.