First build I have made ...please leave some constructive criticism it would be much appreciated. In my opinion attack speed is all you need with Irelia. End game you will just be destroying, with the mandreds, the true damage on your Hiten Style, and your insane lifesteal. Early game don't be too cocky, farm as much as you can with your bladesurge, and it will ensure mid and late game ownage. I level up Hiten Style as soon as possible, because I love the life steal passive and the true damage active is amazing. Attack sequence is Q E W and if it starts getting hairy don't be afraid to use your ult, it will most definately win you fights. team fights, dont rush in thinking you have god mode. Wait for a tank to go in since you have your Q you can jump in and clean up, have achieved many quadra's with this build. Sixth item is interchangeable you could get a frozen mallet for slow and suvivability, or even a black cleaver to tear through their armour, more life steal would make you unstoppable . but I love me my movement speed.
this attack speed build relys on her W, so do not forget to activate it. Irelia is a very fun fun champion and once you get to feel her out she is unstoppable.

Skill up choices
W>R>E>Q
Get Bladesurge at level 2 and leave it there ... it gives you your distance and allows you to farm and farm and farm, getting half the mana back from getting killing blow is nice but your mana does drop Quickly seeing's how you have no Cooldown on it when it lands a killing blow. That is why I get Clarity, I love clarity for early game farming and helps out a lot in the end in teamfights in those moments you need your ult to stay alive but just no mana for it.

Hiten Style:The passive allows you to stay in lane for the most time possible, it even works while your hitting towers. Active is great too, TRUE damgae is TRUE damage and with your attack speed it adds up fast.

Transcendant Blades (ultimate): A little funny to get used to using. Hit R too activate it and then R again each time to send blades of lifestealing death towards your oppponent.The life steal on Transcendant Blades will keep you healed up and tear apart their team. Just make sure to use it in best times possible... great for getting the killing blow on some one who has just flashed away with low health.

Equilibrium Strike: This move is great, very situational though. It is great if some one is on the run, Bladesurge them and Strike them they wont be going anywhere. The disable duration is a nice lenghth, and it is very cool how it can either be a stun or a slow depending on your health compared to target. Very player determined how to use this move though. You do not want to use it early depending on who you are fighting. some one like Jax who just starts wailing on you just wait till his health is higher than yours and stun him, it will be the death of him.

ITEM ORDER
I do not leave my lane until I have atleast enough gold for my basic boots and a Recurve Bow(Farm FARM FARM). Buy your berserkers greaves and Emblem of Valour and now is time you will start to notice dominating. Buy your Mandreds and then rush the Starks, and advise your team you are getting one so you guys dont have 2 aura's floating around there. Get Red buff when ever you can, and jungle as much as you can while walking places. Gold is Gold and it does add up fast. Phantom dancer, this is where it get fun. MOVEMENT SPEED I love it, more Attack speed and Critical strike is always nice. By now you should always be topped up on health with all the Attack speed and Hiten Style passive and your starks, you are a life steal machine. I try to use my ult in the beggining of teamfights when they are all clumped together to maximize damage output, then jump in and clean up activating Hiten Style.

Summoner Spells
These are just what I enjoy using
Teleport: In my opinion a must on any character. Lets you get back to your lane early game for no experience loss. Lets you help rip down a tower in another lane if appropriate. A must to prevent creep waves from taking down towers(great for getting gold and experience)

Clarity: Another great spell in my oppinion. Really great for farming Early game and awesome for team fights.

Those are just my prefferences, Exhaust would be amazing and ignite, but as for summoner skills there is not a MUST HAVE in my oppinion like there are for Fiddles or Nunu.

Runes
Another player choice. I enjoy having the armour pennetration crit damage and Attack Speed, all the attributes that make this build amazing. Those are just what I run with they seem to work for me. Any suggestions I would love to hear them.

Conclusion
Thanks for taking the time to look at my build. It has gotten me countless wins, and a number of quadra kills, I hope it will for you. Irelia is one of the most fun champions out there. My build will help you achive greatness with her. Just take advantage of her Mandreds + Hiten Style + Attack Speed = Win. Please Please Please comment and leave suggestions and let me know how it works out for you.