Avakluon. Hit about 1700 in S2, quit and saw the state of Irelia. Nearly cried. Desperately tried to find some way to help her. Wickd has abandoned her and I needed to rush to her safety. I've mained Irelia since she was released and haven't stopped playing her since. She is the champion I love most and I have seen her through nerfs and buffs and continual states of disrepair. I will continue to play her until I quit this game again. So when I found this build and realised how strong it was, and how many others would suffer alongside myself, I was determined to release it.
Triforce has been broken beyond repair. It is simply not worth buying and anyone who continues to do so needs to stop. What needs to happen now is to take the individual pieces of Triforce and create an entirely new build.
Phage becomes Frozen Mallet.
Sheen becomes Iceborn Gauntlet.
Zeal becomes Zephyr.
Can't teach you how to play her, I just want to offer you a build that may or may not work, it certainly does for me. It's expensive, but that's why I tank up first with Frozen Mallet, then Iceborn and leave Zephyr last.
Flash Ignite is still an incredibly strong combination. Flash Q to initiate is one of the strongest initiates Irelia has. Alternately, due to flash's long cooldown, Ghost is definitely an option. Against a very, very hard lane, take barrier or heal if you absolutely need it. Teleport is also a good summoner, though more team orientated. It could fit your playstyle.
I personally go 16-11-3, because Irelia benefits from the CDR, ArP and flat AD, as well as the AS from the Offense Tree. The flat reduction in the Defense tree, along with the extra HP, Armor is just too good to pass up. The flat Mana regeneration from the Utility tree is extremely good for Irelia, being as mana hungry as she is. Alternately you can put those 3 points into Sunder or Block/Tenacious.
I still like the 15 Flat AD, 13 Armor from S2. And since MR is so hard to buy I still like the flat MR, but Mana regen blues, CDR blues also work. I just think that the Flat AD and Flat Armor are way too good during laning phase to pass up.
BootsI usually go for Tabi, because Zephyr gives tenacity. Use your own discretion; if you need the tenacity now then buy Mercs.
BrutaliserFor when you are dominating your lane, buy it after Phage or Mallet, the CDR, AD and ArP all fit nicely into this build; CDR lowers CD on Q which allows for more Q spamming Mallet/Gauntlet Slow, AD works with Gauntlet Sheen to allow the instacasterminionkill Q, ArP just gives more damage.
Frozen MalletSlow, AD and Health. I cannot stress how important health tanking is in the current season; Armor is almost made redundant due to ArP, MR is incredibly expensive and doesn't offer enough for the cost, not to mention Health was always the best option to tank against burst. The slow is invaluable as Irelia; numerous times in lane the phage proc will open opportunities for kills or heavy harass, and, comes teamfight or initiation, you have the power to instantly slow someone with your q dash.
Iceborn GauntletHoly mother of god this is one of the best items to have been released in S3. Not only does in give us the most wonderful of items, Sheen, but it also gives us CDR! CDR! So good, so beautiful with your Q has a 3.5 second cooldown and no carry alive can escape you. The 500 Mana solves all of Irelia's Mana issues, the AoE Sheen proc just complements her team fighting so well and the Slow. Ohmygod the Slow. The slow coupled with your Frozen Mallet means sure death for almost anyone you catch. The carry is never going to get away. Although Armour is less effective, we still get a whopping 60 armour on top of all of this which helps us against the AD carries.
ZephyrSomeone out there in the Riot Office is looking after us. This item was made for Irelia. Made. Highest Movement Speed item in the game for chasing people down. 50% Attack speed to complement our true damage Hiten style. Even more CDR for Q spams. Even more AD for better Sheen Damage. AND to top it all off, Irelia gets to stack tenacity with her amazing passive. This item isn't the cheapest, but by god it complements her so well.
After you get these three items, and somehow the game is still going, buy Warmogs.
It is probably the best raw tanking item right now and you don't need anymore damage anyway. Unless they focus fire you, Irelia, which means you should win the teamfight anyway, then there's no way in hell you'll die.
Health is King.
If you want more damage, this is the Black Cleaver season, and it gives you more HP tanking.
But by far the most effective damage item is Hydra. You already have a done of AS from Zephyr, and Hydra is the be all and end all of Melee Fighters. But you shouldn't get to this point anyway.