Hey, this is my refurbished Irelia guide, I think that defensive Irelia is too overated, therefore I go for a attack speed build because Irelia's W ability does 75 TRUE damage each hit, true damage means that armour or Magic Resist does not effect it, so basically there is no weakness of it.

Pros

Extremely Fun
Good all round champion
Good Farmer
Heals with W and R

Cons

Squishy Early game
Needs a good farm

Ionian Fervor - In my opinion this is one of the best, if not the best passives in the game, it can help you escape many dangerous situations.

Bladesurge - I get this at level 1, it allows you to last hit minions and run back quickly if you are being held off the creeps by your opponent, also, if your Bladesurge kills something the cooldown resets.

Hiten Style - Suprisingly this is your main damage output ability because of the active which makes it so each hit deals 75 true damage (At max level), it also helps you sustain your lane because of the passive which heals you.

Equilibrium Strike - Use this ability just after you engage, it can easily turn fights around if you are on lower HP then your target because it will stun, and then you will heal a lot while they are stunned because of your W passive.

Transcendent Blades - This is your ultimate, I use this in team fights mostly because if the blades it more than one enemy target it will heal you for more. I also use it early game to clear big minion waves.

Core Build

Berserker's Greaves - This adds to your attack speed, but also gives you movement speed, I get these is all of my matches with Irelia.

Madred's Bloodrazer - Although this item is quite expensive it deals massive amounts of damage, it also helps you to kill more tanky enemies easier also.

Phantom Dancer - This item is a must, whilst giving a huge 55% attack speed, it also gives you some crit, making your auto attacks more deadly, and it also gives you some movement speed which helps you to catch running enemies.

Greater Mark of Attack Speed - These runes just make your attack speed a little faster, they help mostly early game though.

Greater Seal of Armor - These runes mostly help early game as Irelia is usually played as a solo top and she is squishy without armour items.

Greater Glyph of Magic Resist - These just help you be a little more tanky against AP champions.

Greater Quintessence of Vigor - These runes help you sustain your lane more, they also go well with your ulti and W abilites.

I use a 21/9/0, I go 21 in the offensive tree for the attack speed and extra damage, but then I put the remaining 9 into the defensive tree for more armour and health.

For my skill sequence I would usually max my W spell ( Hiten Style) first, but before that I would get one point in Bladesurge, I would also max my ulti whenever possible, and when I can't level my [[Hiten Style I would learn Hiten Style, I max Bladesurge last because it is only really useful for getting to your enemy.

Recommended

Flash - This is a MUST for Irelia (and most other champions), it has saved me from so many different fights, it is also a great summoner spell to catch and enemy, or even juke an enemy to save yourself.

Ignite - Really helps at lower levels when your enemy is escaping on very low hp and running to their turret.

Optional

Ghost - This can save you from being chased by faster enemies than you, it can also help you chase other enemies to pick up a kill.

Exhaust - Exhaust is very helpful, it can turn a fight around or stop and enemy fleeing.

In farming use of your W active can make is much easier to last hit minions if you are low on mana from Bladesurge, although if you are last hitting well with Bladesurge you shouldn't run out of mana too fast because if Bladesurge kills and enemy unit it restores 30 mana and refreshes the cooldown of Bladesurge itself.
When you are level 6 don't be afraid to use your Ulti to clear big waves of minions since your Ulti only has a short CD, it will also heal you for quite a lot if you hit big minion waves with it.

Early Game you should start off by getting Boots and three health pots, you should farm creeps SAFELY until you get around 1700 gold by last hitting with your auto attacks and your Q ability, then you should go back and get your Zeal and a Berserker's Greaves, the Zeal will give you a nice amount of attack speed and it will also build into your Phantom Dancer mid game.

By mid game you should've gotten your Phantom Dancer and maybe even your Madred's Bloodrazer by now, at this stage you should start being able to leave your lane and ganking, note: At this stage in the game you are still quite weak if you haven't got your Bloodrazer.

By the time of late game you should almost have your full build, and you will be VERY strong and most probably be the most powerful in the fight, you should be jumping in and out of fights as fast as you can and dealing tons of damage! If you do this well you could carry your team to victory!

In team fights you should go straight in and deal as much damage as possible, your teamates usually follow in if one person goes in, also if you are tanky it will be hard for your enemies to kill you before your team nuke them. Note: In team fights make sure you go for the squishy targets first! They usually deal more damage.