Hello and welcome to my Master Yi jungling guide!
I had some problems uploading the guide the first time so this is almost a direct copy of my first submission (which saved as anonymous for some unknown reason).
I am Sesasd and I recently started jungling with Master Yi. I couldn't find any successful guides for Yi so I thought that it would be a great idea to make my own.
I will tell you everything about jungling with Yi in this guide and I don't like pointless talk, so without further ado: lets begin!

First and foremost it is important to understand the Pros and Cons of Master Yi before we can continue any further.

Pros:
+Abilities provide great benefits when built right
+Strong throughout the game
+Decent to fast jungle clears (depends on Alpha Strike proc)
+Great mobility
+Decent invader
+Awesome taunt
+Suberb backdooring
+Looks badass

Cons:
-No CC (crowd control skills)
-Weak if chain CC'd (like everybody)
-Noob magnet
-Naturally kind of squishy

[Passive] Double Strike Yi's every 7th attack hits twice. Simple enough. Attack speed helps to proc this more often. Try to use this smartly in the jungle so that you will hit the 7th attack on the creep with the most hp or a creep that would die from 2 hits instead of 1.

[Q] Alpha Strike works as your primary jungling tool and a gap closer. I max this first because it lowers the cooldown on it (so I can close gaps more often) and increases the chances of extra damage on jungle creeps.

[W] Meditate is almost completely useless on jungle Yi. If you get low it won't help you stay alive if you don't have any AP, but if timed just right it can help you tank some immense damage as it increases your Armor and Magic Resist by quite a bit. Meditate can be cancelled by any CC except roots and snares.

[E] Wuju Style is just great. It gives you free damage without any items on it's passive and even more damage when you activate it. You can max this first if you feel like it would benefit you than maxing Q.!!Pro-Tip!! There is a simple trick when using this ability in teamfights. When you activate this and your Ultimate and then kill somebody, don't active the ability again right away because you will have both the active and passive of this skill deployed at the same time (because of cooldowns resetting).

[R] Highlander CANNOT BE SLOWED CANNOT BE SLOWED CANNOT BE SLOWED CANNOT BE SLOWED. Man I love this skill. It gives you insane attack and movement speed on a short cooldown and if you get a kill while this is active, all your skills are ready to be used again! You can also use your ultimate to kill baron/dragon/tower/inhib quickly. It also lets you escape tight spots.

Smite Well yeah. You aren't a real jungler without smite. Use it to secure objectives (Baron, Dragon, Red, Blue) and clear the jungle.

Exhaust You absolutely must get this. No exceptions. It helps when ganking and invading more than any other spell as it:

1. Slows the target if he/she tries to flee.
2. Reduces the target's armor and magic resist.
3. Lowers the target's damage output if he/she stays to fight.

Flash If you plan on trusting your teammates completely that they will win their lanes without your help you can (you really can't) take flash and only have below average ganks. You really shouldn't need flash as it is only used on Yi when you get yourself in a bad position and you really shouldn't get to those situations anyway.

I run this specific rune page to use his kit most effectively and to fix some of his flaws.

Greater Mark of Attack Speed:
Charges up his passive faster and the attack speed from these runes compliments the AD bonus from Wuju Style quite nicely.
If you don't have these or don't want to use Attack Speed marks I would recommend Armor Penetration marks instead.

Greater Seal of Armor:
Mandatory for jungle. Helps with lasting longer in the jungle and also with invading and ganking. A must have.

Greater Glyph of Scaling Magic Resist:
Doesn't help in the jungle but helps early when ganking the mid/top lanes and these are also great mid- and late-game when teamfights determine the course of the game.
If you don't want these runes then I would suggest Attack Speed glyphs for the same reasons I have chosen Attack Speed marks.

Greater Quintessence of Movement Speed:
These are for improved mobility throughout the game. High movement speed is especially important for junglers who have to run around the map helping their team. Movement Speed quints are also great for ganking because Yi has no CC. Also these quints might be the only thing letting you Alpha Strike that fleeing 10 HP Sivir. These are even more important since we are not going to build any other movement speed items besides boots.
If for some strange and unexplainable reason you don't want these quints on your Yi, I would suggest either Attack Speed or Armor Penetration.

Ok this is actually a pretty basic jungling page that works on many champs and not just Yi.

Offense tree [9]:
Summoner's Wrath [1/1]: Improved exhaust, helps with ganking and also late game shutting down dangerous targets.
Brute Force [1/3]: None of Yi's abilities scale with AD and 2 AD isn't going to help you by much. It's a much better investment to put the points in Butcher for faster jungle clears.
Butcher [2/2]: 4 bonus damage to minions and monsters. Slightly speeds up your jungling.
Alacrity [4/4]: 4% Attack speed? Just what Yi needs!
Weapon Expertise [1/1]: 10% Armor pen helps throughout the game. A must have.

Defense tree [12]:
Summoner's Resolve [1/1]: Smite gives 10 bonus gold? I'll take that!
Hardiness [3/3]: 6 more defense to help in the jungle and during ganks.
Tough Skin [2/2]: Pretty obvious, 2 reduced damage from jungle creeps.
Vigor [3/3]: This could be replaced with Durability [3/4] but I like Vigor more since early and mid game jungler moves around a lot and during this time it's useful to regenerate some lost hp before new ganks.
Indomitable [2/2]: Remember that time when you escaped with just 1 hp left? This skill allows that to happen. Also helps in the jungle early.
Bladed Armor [1/1]: Speeds up your jungle clear times.

Utility [9]:
Good Hands [3/3]: There really aren't better options to take so I take this. 10% faster respawn might help you to get to a teamfight you would otherwise miss.
Improved Recall [1/1]: Once again, nothing better to take, saves a second of your time when recalling.
Swiftness [4/4]: This on the other hand is very good and you need this for the same reason you need the Movement Speed quintessences.
Runic Affinity [1/1]: Buff duration increased by 20%. A very useful mastery for Yi since he is a bit Red Buff dependant.

If you have read this far, I thank you. But now you must be confused: there is not a single mention of Phantom Dancers in this guide. That is correct. I do not recommend building Phantom Dancer on Master Yi and to get the explanation we must first look what stats Phantom Dancer gives, and how those stats would benefit Yi.

Phantom Dancer:
+55% Attack Speed
+30% Critical Strike Chance
+12% Movement Speed

Ok sounds great, right? Well... no. Even though Yi benefits from all those stats, we have already covered them with our Runes and Masteries and with Yi's Ultimate Highlander. That is right. Yi's Ultimate is already a Phantom Dancer, so why would we need another one? The cooldown on his Ulti is so short that even that doesn't work as an excuse to buy this item. There are other areas in which Yi needs help with and we should concentrate on making those areas stronger instead of just giving Yi something he already has.

Now that we have that covered, let's get to business. Yi needs 3 basic things the most (from items): Attack Damage, Armor Penetration and Survivability. These items do the job the best:

Wriggle's Lantern is an obvious choice and a very strong item on Yi. You can clear the jungle even faster, you get a free ward plus extra armor and damage for stronger ganks. You will can later sell this item for a Bloodthirster.

Berserker's Greaves is a very good choice for Yi as he gets more attack speed and the item itself is very cheap so getting early boots for better map control is this easy!

Mercury's Treads also viable on Yi if the enemy team has too much CC for your liking. However picking Yi against enemy like that might not be the smartest option. Anyway buy these boots if you feel that snares and stuns are holding you down.

Warmog's Armor is one of the best items in the game! I usually build this right after I have my Wriggle's and boots finished. You get so tanky that the enemy just can't kill you while you still dish out great damage. When you are still building Warmog's your damage output is at it's weakest compared to early and late game but don't worry, you will be happy that you bought this item.

Frozen Mallet if your team has absolutely 0 CC build this instead of Warmog's. I still build Warmog's 9/10 games. The slow might help a bit but after you have your Ulti you can chase anybody down.

Atma's Impaler is built right after Warmog's Armor or sometimes after Giant's Belt if your team is doing really well. If the enemy team has a heavy AD team you might want to build Chain Vest even before finishing Warmog's. After you get this item there is absolutely no stopping you.

Last Whisper is the item I usually get next, even though if they start building armor very early you might want to build this item much earlier. Last Whisper gives crazy damage combined with your E and Ultimate so do not underestimate this item. This item can be rushed even when other item's are not finished, because if the whole enemy team is already building armor when you just bought your Giant's Belt, you are going to have a bad time. This rarely happens though.

Black Cleaver is a better Armor Penetration item early game, but Last Whisper wins late game. As Armor isn't built that much early, I really don't recommend this item. This item also has more expensive parts but it can benefit the AD carry of your team if you both attack the same target.

Banshee's Veil is the item for you if you still for some strange reason don't feel tanky enough or you get caught by CC. You are so unkillable after you have this item combined with the rest of the build that it's not even funny.

Maw of Malmortius is the other option for Magic Resistance. If you team is stomping the enemy buy this instead of Banshee's as this item gives very nice damage plus a shield that absorbs magic damage. Also makes you more deadly when on low hp.

Force of Nature You actually might want to consider this item as your MRes item since it gives you a ton of resistance, some movement speed + with your high hp pool the health regen is quite nice. I'd still only consider buying this if the enemy team is super heavy on AP.

Bloodthirster is your final item which will take the place of Wriggle's. I have honestly never had a game long enough for me to buy this item but if it ever happens, this is the item to get.

Elixir of Fortitude is great whenever you feel like a teamfight is coming or you want to contest Dragon/Baron. Also buy this when you finish your itembuild.

Elixir of Agility is pretty much the same as Elixir of Fortitude, but if you only have money for one of these, buy Fortitude.

Elixir of Brilliance if you have absolutely nothing else to buy, get this. Yi's Q and W have AP ratios so it isn't completely wasted.

Oracle's Elixir if the enemy is warding heavily during early game you might want to get Oracle's to clear wards and make ganking easier. It will also piss the enemy off quite nicely. This will make you a major target however.

Sight Ward I usually buy 2 of these every time I shop, even after I have Wriggle's. They are always useful.
!!Pro-Tip!! Can also be used when opponent Flashes to other side of the wall so that you quickly place ward where you think they flashed and then Alpha Strike them now that you have vision of them.

Start with Cloth Armor and 5 health potions. This gives you plenty of sustain in the jungle + the ability to gank without the fear of being killed yourself. You can also challenge the other jungler to a duel with these as your starting items.

Standard route:
Start Wolves -> Blue -> Gank if possible -> Wraiths -> Red -> Gank if possible -> Golems/Enemy Wraiths

Continue clearing your jungle but prioritize ganking, even before lvl 6. Yi is surprisingly strong early.

Alternative route:
Wolves -> Blue -> Enemy Red -> Gank -> Give your Red to your top/bot if possible or take it yourself so the enemy won't get it

Teleport back to base when you can afford Boots, Madred's Razors and a couple of wards. This shouldn't really be a problem as you can easily get first blood with red buff and exhaust. When Blue spawns ask if your mid wants it, unless they don't use mana in which case you can take it yourself.

Continue jungling and ganking and try to feed your lanes some kills, even though you getting kills is not a bad thing either since you can also carry hard. It's just easier to win the game with a couple of decently fed champions rather than one super fed.

This should be enough to get you started with Jungling Yi. I wish you luck and glory on the battlefield. Lastly I'd like to show you some end game scores to prove that this guide really works! (Oops, a Janna game in the middle xD)