Introduction

This is my first guide, and it's a build I've been personally working on, and it seems to work well for me. I don't play ranked games yet, but if someone wanted to try it in a ranked game and let me know how it works, that'd be awesome.
Updates and Credits
v1.01:
Added "Abbreviations and Game Play Terms" Section.
Added "Other Viable Items" Section.
Credits:
Thank you lexiphanic, for the feedback, and guide tips, as well as recommendation for "Other Viable Items" section.
Abbreviations and Game Play Terms
AS - Attack Speed
AD - Attack Damage
LS - Life Steal
CC - Crowd Control (Stuns, Snares, Roots, Silences, etc)
DPS - Damage Per Second
AP - Ability Power
Chasing - Chasing after an opponent.
Tower Diving - Running within range of an enemy turret to get a kill.
Pro's and Con's

- Relatively fast jungler
- Built in on-hit healing
- Amazing ganker
- Good chaser
- Amazing DPS output late game
- Passive reduces CC

- Can get rather squishy without defensive items
- Late game, you get focused down
- Stun only works when you're at a lower HP% than your opponent
- Expensive items
- Dependent on kills
Masteries
I choose 21/0/9 for jungling. Allows for easy ganking.
Items
- Start with
Cloth Armor and 2
Health Potion for opening jungle. If you're comfortable with your route and your leash, you can stick with 1
Health Potion and be completely fine.
- Next, pick up
Madred's Razors, as
Wriggle's Lantern is too good for jungling not to get.
- Pick up a
Boots of Speed or
Berserker's Greaves for the AS, unless they're CC heavy or AP heavy, then pick up
Mercury's Treads. Your call on this one.
- After your level 2 boots, finish
Wriggle's Lantern for the LS and the free wards. The jungle is yours now.
- Your next goal is building towards
Trinity Force. Again, the order of which you build is your personal choice, but I get
Phage first for the slow, health, and AD. Afterwards, it's normally situational on whether I want to move faster and the AS of
Zeal, or
Sheen for it's Proc. Both are equally as viable in my opinion. Remember that
Bladesurge is an instant proc from
Sheen, so use that to your advantage.
- After
Trinity Force, I start building my
Zeke's Herald, for the LS, and AS. I get
Recurve Bow before
Vampiric Scepter because attacking faster heals you more than the VS, and with On-hits for
Phage, their is no escaping you.
- At this point, you can sell your
Wriggle's Lantern if you want, for a faster
B. F. Sword, since you should be more present in lanes and you now have the LS from
Zeke's Herald. Use the
B. F. Sword to build towards
The Black Cleaver, for the AS, AD, and the armor reduction. This is about the time where people start to hate you.
- Your last 2 items should be
Infinity Edge for the AD and Crit Damage, and
Phantom Dancer for the Movement Speed, Crit Chance, and insane amounts of AS. You should now be near unstoppable in any 1v1 as long as you CC right.
Other Viable Items
The Bloodthirster is an awesome item when it's fully farmed, and if you can spare the AS, you can substitute
Zeke's Herald for this, if your team has another person with
Zeke's Herald, or a lack of AD characters.
Madred's Bloodrazor is also a really good item for
Irelia, since it provides a decent amount of AD, a large amount of AS, and some armor to boot! Not to mention it has an awesome proc for eating away those tanky toons. You can substitute
Phantom Dancer or
The Black Cleaver for this.
A More Tanky Bruiser Item Build
If you're aiming for more survivability, than by all means, grab a
Warmog's Armor and
Atma's Impaler. The two work beautifully together, and you'll find yourself staying alive much longer in team fights where there are more AD based characters, and also give you a good amount of AD in the meantime.
If they are throwing a lot of AP your way, with hard-hitting nukes, grab a
Banshee's Veil for the MR and the spell negate.
You can also grab a
Hexdrinker for champions like
Karthus, which will ease his
Requiem by a lot, and you'll walk away more often.
Guardian Angel is also a good choice here, for the armor, magic resist, and the built-in revive. Oh, they thought they finally killed you?! Let them think again!
Skill Priority and Reasoning
Passive:
Ionian Fervor - Reduces the duration of stuns, slows, taunts, fears, snares, and roots for each nearby enemy champion. 10% for 1 champion, 25% for 2 champions, and 40% for 3 champions and above.
Priority should be your R
Transcendent Blades. The blades shoot wherever your courser is aimed, so make sure you keep your cursor over the target, or predict where they may move to.
I max W
Hiten Style first, because you're jungling, and the healing/true damage is a must.
After W, I max out E
Equilibrium Strike for a more reliable CC.
Lastly, I max Q
Bladesurge, taking one point at level 2 as a gap closer.
When engaging, you should always pop W
Hiten Style for the extra True Damage. Luckily, activating Hiten Style doesn't negate your passive
Ionian Fervor, like Yi's does. Try not to open with Q
Bladesurge, unless you're picking off a low health opponent, or you really need to get into the opponents face fast.
If you can, save your E
Equilibrium Strike for a stun if they start wacking you hard. Use your Ult
Transcendent Blades] if they run with low HP, or if you're by creep waves, for extra Life Steal.
Summoner Spells
Smite is a must for jungling.
I take
Exhaust, with the Mastery for it, to turn the tides of battle in my favor, and retreat if I must.
Other acceptable Summoner Spells:
1.
Ghost - Chasing made easy.
2.
Ignite - Always nice to have a bit of extra damage, but you shouldn't necessarily need it.
3.
Surge - More Attack Speed? Why not?
4.
Teleport - Allows for getting from one side of the map to the other quickly to gank.
5.
Flash - Flash is always useful for escaping/chasing.
Non-acceptable Summoner Spells:
1.
Garrison - You're not a support/tank. Unless you Tower Dive a lot, you shouldn't take this.
2.
Heal - You really shouldn't need Heal, because of the Life Steal that you have.
3.
Revive - Specced into Good Hands, and if you're doing well, you shouldn't die much, anyway.
4.
Cleanse - Your Passive gives you CC reduction, and if you grab Merc's Treads, it stacks with the passive, so CC should be practically negligible.
5.
Clarity - I don't really run out of mana, since I'm jungling and have Blue Buff up a good amount of the time.
6.
Promote - Why would you use this as a jungler?
7.
Clairvoyance - This could be helpful, but I never tend to use it, because supports normally run it.
Creeping / Jungling
Get a Leash for Blue Buff, and continue to Wolves, Wraith pack (
Smite blue wraith), Double Golems, Wolves again. Go back to shop, should grab
Madred's Razors. Red buff after
Madred's Razors and then continue on with normal route. Grab Dragon as soon as you can, normally around level 7 if you have a
Health Potion left.
Once
Irelia reaches level 3, and grabs her second point in
Hiten Style, you don't really need pots for jungling, so save whatever you have for Dragon and/or ganking.
Once you hit level 5/6, you can start ganking effectively.
Mid/Late Game Irelia
Mid Game: Once you get
Trinity Force, you become a serious threat to any lane, more so if you have competent team mates. Ganking is extremely important, so do that whenever you see anyone over-extended, or if your team mates could use some help. Never turn down a kill, unless you're unsure of where opponents are on the map. This is where those wards from
Wriggle's Lantern come in handy.
Zeke's Herald just gives you and your team the AS and LS to end fights in a much cleaner manner.
Continue to jungle when not ganking, unless there are lanes to be pushed or kills to be earned.
Late Game: FARM, FARM, FARM! Late game, your items are a bit more expensive, so you want to complete it as soon as possible, right? Get that gold. Farm kills, creep waves, and jungle camps in that priority. Grab Dragon whenever up. Once you complete your build, buy some elixirs, and enjoy seeing people rage.
Closing Statements
Irelia is an amazing character, with a lot of potential. Have fun face-rolling whole teams with the amount of Life Steal and Damage output you have. Remember, it's not fun till you "Ace".