After recent changes on Irelia (nerf of heart of gold, spirit visage and spells) the way Irelia has to be built does not consist of getting fast Trinity Force

This build makes you an offtank dps god and be almost imuned to AP heroes. Once mastered, this build is deadly in ranked games (for low to high elo).
It fits perfectly in current metagame.
I recommand a solo top lane for her (see http://www.mobafire.com/league-of-legends/build/offtanks-the-new-metagame-79701 to know why)

See WickD stream for demonstrations, he used to build here like that (http://clgaming.net/live/304)

IN PROGRESS :)

Notes
- Icons added
- add Runes chapter

Doran's Shield
Good start for laning survivability and life regeneration

Boots of speed
=> At this time you have to buy pots and wards to lane efficiently

Wit's end
This is the perfect item in this build combine to your W and he gives you MR also

Mercury's treads
Because AP carries rapes now and it stacks with your passive
It can be replaced by Ninja Tabi if you really have to, hence, if you face 2 3 AD carries.

Spirit visage
Perfect synergy with her. Life, MR, CDR and better life steel !

Chalice of harmony
=> you think i am dumb ! No... This item is very very cheap and gives you MR and the most efficient mana regeneration in the game. Thus, you can spam your skills at lane and control perfectly top.

Hexdrinker
Good overall item. Could be replaced by Thornmail if there is too many AD.

Aegis of the legion
Replace Doran's Shield by this ! good overall item also

Trinity force
Replace Chalice of Harmony by this. No need to say more on this, you should probably now everything about it.

- First max Hiten Style because it is your main regeneration during laning phasis. This is also, combine with Wit's End, a wonderful damage oupout when you auto attacks.
- Then max Equilibrium Strike : good damage output and slow/stun. 1 point at lvl one to avoid diving or keeping your *** up if someone is chasing you.
- Finally Bladesurge : 1 pt at lvl 4 only to help you farming/chasing enemies. Don't forget that you can use it to escape from a fight by targeting minions !

3 x Greater Quintessence of Fortitude to bost survivalability and improve laning phasis.

Greater Mark of Desolation9 x Greater Mark of Desolation is an obvious choice here. It benefits your AA and your Bladesurge

9 x Greater Glyph of Warding to bost survivalability and improve laning phasis as Quints do.

9 x Greater Seal of Resilience brings a nice armor bonus at the begining that helps your laning. You don't have to pick mana regeneration because of Chalice of Harmony in this build

Flash

Best spell in the game.
- Deadly when uses offensivly
- Best escape

Ignite

Shutdown some heroes like Vlad, Swain, Tryndamere... great damage also

Exhaust

Good pick also (pick enhanced exhaust with it)
Shutdown AD carries : this is the what you needed if theer is more than 2 or 3 AD carries in the game !

Pros

- God mid/late game
- Almost imune to magic damage
- Lot's of true damage, works on everyone
- Perfect in current metagame

Cons

- Require mass farm
- ... that's all ?

Farming is the most important thing with this build.

Early game
Last hitting only. Do not push your lane at all or you can be traped by the jungler or stuck into brushes. At lvl 4, Bladesurge helps you to last hitting but keep your mana up.
Lvl 6 : you ultimate Transcendent Blades is a blessing : you can push so hard by killing an entire wave of minions with it and get a nice life regeneration.
Irelia is pretty squishy early game so be careful and play safe.

Mid game
Keep farming a lot and add bleu/red buffs in your farming
At this point, you should be capable to handle your lane without any problem. You can poke really hard with your Q/ E/ W combo.

Early game
You should not be very agressive... focus on farming.

Mid late game
If you opponent approach you too much use E-> W and poke/chase with Q.

Of course you can add you ultimate Transcendent Blades in all combos :

• Focusing minions for life regeneration if they are here
• Focusing enemies if chasing