Hello and welcome to my guide :) This guide focuses on making Irelia hard to kill while her damage is high. We do that easily through Trinity Force, and bloodthirster. This build focuses on being able to be tank like with major damage (Trinity Force + Bloodthirster.) while stealing tons of life back as well as having defensive items.

TL;DR
This guide, while expensive, will give you tons of lifesteal/damage with decent surviving stats.

Pro's Almost impossible to towerdive due to stun. High survivability Great farmer Fun to play People rage at you She doesn't need to hold her blades xD

SPACE

Con's Item dependant (in this guide) Costly (but your a great farmer :D) Counterable with armour. NEEDS the tenacity boots. You survive through lifesteal/passive, you get stunned, you will probably die.

Skill Sequences; When and Why?

Equilibrium Strike
I max out Equilibrium Strike first because I find it the most useful; It is your only form of CC and depending on when and how you use defines its usefulness. It gets a longer stun which means its more utility. More chance of surviving a tower dive + maybe netting yourself or an ally a kill. 2 seconds under the tower is very daunting to level 9 champions.
It also has a decent slow. Nothing too fancy, but it gets the job done.

TL;DR
Nice damage. Nice stun. Nice slow. Nice all-round powerful weapon against that annoying warwick.

Hiten Style
I max this second because of the damage you can do with it. Sure, the healing is great, at low levels is what you use it for, that and a bit of AA bonus, but late game, if you picked ignite, activating Hiten Style then adding ignite will make tanks scared to vs you, they can't stop it, unless they stack health, if they stack health, their Armour/magic resistance will gradually become lower. (unless its Rammus, he will just run into you regardless)
This spell also has PERFECT synergy, this spell is what made me want to try out a life steal build. With trinity force you get nice attack speed, with life steal, you get tons of health back + 26 health. 26 health is quite a lot, i have taken down towers because they hit me for 90 or so (With Armour) and its not on-hit, so it could for towers too. The tower died first, just saying.

TL;DR
Max second because of nice heal + amazing true damage against the usually beefy people taking top lane.

Transcendent Blades
We get this whenever we can. This just adds to your; sustain, kills, troll factor.
This abilities cooldown is SO short, it's unbelievable, which makes it a great thing to do if someone is getting away with hp that is SO close to 0 that you just have to chase them. (We all know this mindset, just saying.) Just use your ultimate, watch them rage and use the 3 other blades to take out them minions regaining a high amount of HP.
It can be used for pushing, if you need hp, finishing blows.

TL;DR
Max whenever you can. (3rd)
Amazing utility, lots of ways to use it. +troll factor if you kill someone with it.

Bladesurge
We level this last.
I haven't got a good word to say about this, it is decent for last hitting?
Basically, this is your initiator/catching spell. With your damage late game, they wont get away or with your stun/slow they shouldn't. This spell allows you to catch people, cover long distances or even pull off some nice stunts. That is all

TL;DR
Not much utility. Your get-in/get-out spell.

This is why I use these 2 spells, summoner spells are however, which you prefer.

Gives unitwalking (Walk through minions/units) Increases mobility (Irelia is a mobile character, she needs mobility) 35% more movespeed to go to different lanes/get into your own. Downfalls Doesn't have as much utility as flash Quite long cooldown Slows still affect you.

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True damage (100% magic/armour penetration) Scales nice into late game. Halfs healing/health regeneration effects. (Useful against healers like Soraka) Nice little animations ^^ Downfalls It IS possible to click the wrong person. Cleanse and Quicksilver Sash can dispel it. Doesn't actually STOP heals, just halves them.

Irelia is best going solo-top. She is a GREAT farmer (with her Bladesurge /auto attacks and later on, her Transcendent Blades
This build is very expensive and you should be farming as MUCH as possible in your lane, going into the jungle and clearing mobs, going to gank champions etc. as long as it's okay with your jungler, this build is primarily a solo-top build, it isn't possible to (unless laning with a babysitter) farm as much as you need for this, though when you get randuin's omen, you will practically be complete, Guardian Angel is just the icing on the cake.

TL;DR
Farm as much as you can. Go solo-top. Gank a lot.

Irelia is a very sturdy champion, with this build she can easily take (unless they chain-stun) 2-3 champions.

However, this section will cover 1v1.

Irelia will want to open with Bladesurge mainly because its a gap closer and if they look at your items, they will try to run. (Not a humorous comment, i'm serious, xD) After that, use Equilibrium Strike, people will argue saying Hiten Style first, but you can't kill something that is running, you may be fast, but attack animations won't be as fast, then you activate Hiten Style after this, you should melt them. Use Equilibrium Strike and Hiten Style whenever possible, but save Bladesurge in case they try to run and you need to finish them off.

Irelia SHOULD gank. With this build, you should gank WHENEVER you can (not if your lane is in trouble, if your lane is at their turret and that delicious annie is about to recall with 20hp.

Ganking is straight forward with Irelia, if someone in your lane has CC, tell them to use it, exhaust is fun too. Then, you Bladesurge -> Auto Attack -> Equilibrium Strike -> Auto attack -> Hiten Style -> Auto attack. (Then if needed -> Transcendent Blades and/or Ignite)

Why auto attack? Because you have trinity force a.k.a Auto attack steroids.

This will get you or an ally a kill. This will get their laning partner paranoid, as well as the other lane to you, (You will mostly be top, so bottom lane/mid lane (whichever you didn't gank) will get paranoid that your coming for them. This will also cause arguments in their team, "Why didn't you say SS, does she just leave lane randomly and enter again when she pleases?!" etc. Which is great, (i know, i'm the plague of LoL for this but; if they argue, they won't help one another, which means your team will be more synergistic than theirs/ better in team fights. Just be careful how much you stir, it is still a game and your enemies ARE still people, ;).

Escape artist
Due to Irelia's mobility, it is extremely useful to use this trick;
If your running from 2 maybe 3 enemies at low hp, a good trick is to (this takes time to learn) run backwards after a bush and stun your first pursuer, then bladesurge to the furthest enemy away and run that way. This will buy you time, but because you run so fast, they will not bother to chase you.

Hiten Style: Towerkill
While this may seem stupid. Near the end of this guide, You should activate Hiten Style when taking down turrets. Turrets have some armour, and the reason i didn't take Siege Commander is because you don't need to take armour away when you can slice straight through the armour.

December 7th 2011:
Published! :D
-- Added Wit's End. Took out Reverie. Replaced a swiftness rune with flat health quint. Took out Vampirism + Havoc and added juggernaught & Mercenary
-- First +1 vote :D

December 8th 2011:
Tested without Hextech Gunblade and with Guardian Angel went alright. Switched them around.
Kept the level up sequence.