This is my third guide and its on none other than Riven - Miss Spamalot
I think as some others that Riven is best suited for jungling. But I haven't found any jungling guide that works for me so that's why I tried my own build. And after about 30-40 Custom games, this is what became the final result.

IMPORTANT: This guide is still under construction but I still want to share it so I can get some good criticism while I finish this guide.

Abbreviations:

AA = Auto Attack
AD = Attack Damage
AP = Ability Power
AS = Attack Speed
BC = Black Cleaver
CC = Crowd Control
FM = Frozen Mallet
MR = Magic Resist
TF = Trinity Force
Q = Broken Wings
W = Ki Burst
E = Valor
R = Blade of the Exile / Wind Slash

First Path
Second Path
Third Path

I have a one guide, if you can get leash on golems. And one, if you can't get leash on golem. Both works, and both will take the same amount of time. You will be level 6 with Wriggle's Lantern at 9:00-9:30. The only downside to jungle without leash is that you will have less hp when you jungle. Which means you will be more vulnerable to counter junglers.
Don't forget to use you skills to move, when you travel from one creep spawn to the other.

With leash

1. Buy 4 health pots and spec Q. Then go to the golems. Here you will need someone to leash and help you with a few hits. Use 1 pot.

You and your buddy should stand like this to make it optimal.The golems will need to walk further before they turn and attack you, resulting in more damage on them and less on you. Don't forget that your buddy need to hit a few times or you'll die.

2. Spec E smite the blue wraith while initiating with E followed by Q and AA combo. Use 1 pot.

3. Initiate with E follow by Q and AA combo. Use 1 pot.

3½. Spec W. Here I try to kill the small creeps on blue. Try not to die but if you do its not that bad. You will respawn after 13 seconds and it will take 8 seconds to recall and 3 to reg so it will be about the same time spawn that you will lose.

When your back at the base you want to buy 2 more health pots and a Vampiric Scepter. Now head back into the jungle.

4. Smite the blue wraith and kill the rest with skills and AA. Don't use pots.

5. Kill the wolves with your combos. Don't use pots.

6. Spec E then take blue buff and queue 2 of your remaining pots use the last one if absolutely necessary. Smite at 550hp to be sure that it won't be stolen.

7. Take out golems. Use pot if necessary. Then port back.
Now you should be able to buy both Long Sword and Cloth Armor and hopefully another pot.

8. Smite the big wolf and kill the other wolves with your combos. Don't use pots.

9. Kill the blue wraith first. Don't use pots.

10. Go and take red and use all you remaining pots.

11. Kill golems. You're now level six, recall and buy Wriggle's Lantern

Without leash

1. Buy 4 health pots and spec Q. Then go to the golems. Smite on of them then kill them with Q. Use 1 pot.

2. Spec E Initiate with E follow by Q and AA combo. Use 1 pot.

3. Smite the blue wraith while initiating with E followed by Q and AA combo. Use 1 pot.

When your back at the base you want to buy 2 more health pots and a Cloth Armor. Now head back into the jungle.

4. Spec W then take blue buff and queue 3 of your remaining pots. Smite early so smite will be ready again on the blue wraith.

5. Kill the wolves with your combos.

6. Smite the blue wraith and kill the rest with skills and AA.

7. Take out golems. And port back. Now you should be able to buy both Long Sword and Vampiric Scepter. (You should not be able to buy a pot if you have been fast enough but if you can, then great buy a pot and use it on the red buff)

8. Smite the big wolf and the other wolves with your combos.

9. Kill the blue wraith first.

10. Go and take red.

11. Kill golems. You're now level six, go back and buy Wriggle's Lantern

I have tried 3 different starting builds.

First one was just a Vampiric Scpeter Failed. You just don't get enough life steal at level 1-3.

Second was 4 pots and a Cloth Armor, it works but you can't buy anything other than more pots on the next recall.

Third was just 4 pots. It sounds a little weird but it works. Because don't need the extra armor from Cloth Armor to survive the first path. And you get you Vampiric Scepter at level 3, which is good. I prefer this way because you can leach hp on lanes if you need to hold mid for someone.

I don't know if there is any way that is better that 4 pots. Thoughts, questions and improvements can be posted below. Because I am still testing this build.

After your starting jungle is done and you have Wriggle's Lantern and Ionian Boots of Lucidity's. Then you are free to chose your own items depending on the situation.

The Items after Wriggle's Lantern are the items that I think would fit in most situations.
This is why I choose these items:

Ionian Boots of Lucidity's: You need the cooldown reduction. Enough said. You could use Mercury Threads if they have a CC heavy team

Frozen Mallet: The slow is good because you are a great chaser and with this you will help you teammates catch up in a chase. But the most valuable is the health. You are kind of squishy early game and you need the extra health.

Black Cleaver: Great item, first of you get armor pen. Then you get damage, and you get AS. Some would say that AS is bad on Riven, and I agree. You should be able to hit between you skill combo and in that way utilize your AA. And because you do you skills "between" your AA you wont need AS. So the AS you get from BC is a waste.... not! Even if you don't need the AS when you can land you combo. You will need it when you don't. Sometimes you need you Q to close the distance between yourself and the target. At this time you will be standing close to the target with all you spells on cooldowns with 3 stacks on you passive that you couldn't use because the distance was to far. Now the AS will make difference. But this doesn't happen that often so the AS on BC will be enough, so don't buy more AS.

Why not buy Yomuu's Ghostblade if you want AS and armor pen? Yomuu's is a great item. BUT you need more damage. To buy both Frozen Mallet and Yomuu's will give you to small damage output mid/late game. And you can't afford this.

Bloodthirster is mostly bought because of the damage but the extra life steal is great.

I included Infinity Edge in my guide before but I removed it and filled its spot with another Bloodthirster. And I did that because Riven doesn't get that great benefit out of crit since she doesn't auto attack as much as champions like Ashe and Master Yi. She will get a great benefit out of more damage. That's why I choose another Bloodthirster because it was 860g cheaper and you get more damage out of it. I won't go as far as saying that Infinity Edge is a bad item it isn't but it can be replaced with other more suiting item.

You could skip one of the Bloodthirsters and buy something more tanky. Because you don't get life steal on you skills, which gives more life steal a small drawback. If you look in a survivabilities point of view.

Some of you might have notice that I don't have a single MR item. And I know that it is a flaw. But I rely on valor and the high damage to help me kill nukers faster than they kill me. I haven't played enough games to see if this works or not. But if you feel the need for more MR I would recommend either Hexdrinker a cheap good MR item on Riven, or Force of Nature because of the extra health reg and MR which is great but also the 8% Movement speed passive that will help you with chasing and escaping. But I don't recommend Banshee's Veil. Yes its a great item but you don't benefit from the mana. I think Force of Nature will be a better choice since its cost is about the same you get more MR and you Valor is like a Banshee's block the damage of 1 spell (not stuns and slows but hey buy Mercury Threads to get some Tenacity)

Why don't you include Trinity Force in you guide?

This is why I don't use trinity force:
1. You don't need the AP
2. You don't need mana
3. You don't necessary need more AS
4. You don't necessary need more movement speed. It's good but you don't need it.
5. Sheen is good! But it has a cooldown on 2 seconds. And will this really boost your damage output, better than pure damage items. Look down below on Black Cleaver Frozen Mallet vs Sheen/TF for more info and calculations

I think that Black Cleaver and Frozen Mallet is better than Trinity Force this is why:

TF stats that's good on Riven:
+30 AD
+30% AS (occasionally)
+15% critical strike chance
+250 health
+12% movement speed (occasionally)

TF Passive
Passive Unique: On hit, 25% chance for target to be slowed by 35% for 2.5 seconds.
Unique: On cast, for 10 seconds, your next standard attack deals extra damage equal to 150% of your base attack damage. 2 second cooldown.

Cost: 4070g

BC and FM stats that's good on Riven:
+75 AD
+30% AS (occasionally)
+700 health

BC and FM Passive
Passive Unique: On hit, target suffers −15 armor for 5 seconds (maximum 3 stacks).
Passive Unique: On hit, target is slowed by 40% for 2.5 seconds.

Cost: 2865g + 3250g = 6115g


Black Cleaver Frozen Mallet vs Trinity Force
BC FM:
Better slow
More damage
Armor pen
More Health

TF:
More Movement speed
More Crit chance
Sheen
Cheaper

Rivens skills in detail:

Passive Runic Blade: (Innate): Riven's abilities charge her blade, causing her to do 5 / 7 / 9 / 11 / 13 / 15 (+0.5 per bonus attack damage) bonus physical damage on her next autoattack. Riven can store up to 3 charges, and will only expend one at a time.

(This will mean that with BC and FM you will do 22,5 more damage than the passive will if you have TF.)

Broken Wings: Physical Damage Per Strike: 30 / 50 / 70 / 90 / 110 (+0.6 per bonus attack damage)
(27x3 more damage)

Physical Damage: 50 / 90 / 130 / 170 / 210 (+1.0 per bonus attack damage)
(45 more)

Minimum Damage: 80 / 120 / 160 (+0.6 per bonus attack damage)
Maximum Damage: 240 / 360 / 480 (+1.8 per bonus attack damage)
(About 50 more damage)

Calculations:
I won't count with The BCs passive and the 20% damage on the skills from the ulti. But I will count with Rivens max base damage in an attempt to close the price gap that's 2045g between TF and BC + FM.
And I will only count the differences in damage not total damage

Combo with BC FM: 635 (R + Q 27 + AA 54 + Pa 22,5 + Q 27 + AA 54 + Pa 22,5 + Q 27 + AA 54 + Pa 22,5 + E 0 + AA 54 + Pa 22,5 + W 45 + AA 54 + Pa 22,5 + R 50 + AA 54 + Pa 22,5)
Explanation: AA damage is higher because of BC and FM and ulti. The rest is just the boost you get on all your skill because of the increase in AD.

Combo with TF: 621 (103,5x150%x4)
Explanation: You will get 4 stacks of TF with in the time frame of you combo.

Summary:

BC and FM will give you better stats than TF and the boost you get on you skills because of you increase in AD will overshadow TF/Sheens Passive. Thats why I don't include TF in my guide

I have chosen these runes because it will make your jungling faster (and possible) and you will still get some good benefits out of them late game. First the AD stacks on all you skills and the cooldown reduction is just awesome because you don't depend on mana. So I don't think there is any other runes that would work better than these.

Nothing weird here you spec 9 in utility to maximize your jungling. Spec greed it will be the difference between a health pot or no health pot.

21 points in the offensive tree. It makes your jungling even easier.

I chose Smite and Flash because sometime you need the extra utility that you get from flash, like jumping over a wall. You could use Cleanse or Ignite instead of Flash. It would be a valid choice.

But Ghost isn't, you just don't need it you get a lot of mobility with your Q and E and you should be able to out run most chars with those spells.

Any other Spells you can use? No, the rest is just not for you.

I have seen some other skill builds and I have tried these. And I will explain why I choose the one above.Here we have a build where you max out Q very early. This will indeed give you more early game damage output. But it will make the jungle a little harder since you are going to have less hp when going around. Which will make you more vulnerable to counter jungling. And you won't be able to do the "jungle without leash". I would not build Riven this way. Because your damage output from level 6-11 ain't that great without proper items. So even if you boost your q early you won't get more kills out of it. I think that Rivens role is to assist the lanes with ganks between level 6-11. Where you either kill steal or just slow them down with your stun and knock back. And you should go around farm. Because Riven is at her best at the higher levels. When she can spam her skills a bit more and when her damage output doesn't merely rely on her passive.

I read at a forum that a guy stated that you should max W first for maximum damage output early.


Now why is he wrong?
He isn't, this will indeed maximize you damage output early. But here is the drawback you will rely on a very unreliable skill. Everyone that have played Riven knows that her W have ridiculously small range. What if you miss? You whole damage output will go out the window, is it worth it? And you need level 5 + 20% cooldown to make it possible to W before and after the Q combo.

This is the skill build that I have choose to play with, why?.
Because your jungle will be a lot easier with a few more points in E and you will get a more consistent damage output if you maximize your Q first. Then I place 2 points in W to lower its cooldown. This might not be the best build but I think it's pretty balanced. And thats why I choose this build.

This is not a finished guide, but you can still rate it and comment. So please do.

If you think that there is missing a chapter that you would want or you have any other request on what I should do with this guide then please comment below.

Special thanks to EldRaven for helping me with jungle paths and to Lithium769 which jungle guide I got some of my ideas from.