Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
I've been playing Irelia from the moment she was available for purchase, and she's all I've played since. I've tried every build type, some would work, some would flop, most would be just ok. This build had proven to be the most effective for me.
The focus here is AS and Health.
Abilities: Hiten (W) Style is basically free life steal. Get it first, it'll help you stay in lanes much longer. Next, you have Equilibrium Strike (E), which is a great offensive AND defensive ability. Getting this second will better your chances to get an early kill with your lane parter. Use it to slow them down or stun them if the appropriate Health % allows. Next we have Bladesurge (Q). This is your fight initiator. Mid to late game it can do a good chunk of damage on its own. Your ultimate, Transcendent Blades, is generally underestimated by a lot of people. I don't how many times I've been able to kill the opponent with TB as they fled from utter surprise and horror at the beast that is Irelia. Order of attack is Q-E-W-R. Spam your ultimate as you auto attack, being sure to spam your other abilities as they come off CD.
Early game: Get a Dagger and a health pot. The Dagger will provide a bit of AS for Hiten Style. The faster you hit, the more you are able to heal yourself. Try to play as defensively as possible. Irelia is quite squishy, so stay back and strike if you can do so safely. As soon as you have enough money and are in a good spot to do so, port back and get Berserker Greaves. At this point you should be LVL 3-4. Now you can start being a little more aggressive. Get with your lane parter, coordinate a strike, dash in, slow/stun, and pop Hiten Style. If you have to, throw an Exhaust of them. Most times this is enough to kill the enemy. As soon as you have 1050 gold, port back and get Recurve Bow. Finish it with Sword of the Divine as soon as possible. This is where you'll start seeing how powerful Irelia can be.
Mid game: Start working on Madred's Bloodrazor. This is a great utility item as it provides AS, AD, and anti-Godzilla HP. There is absolutely nothing I would consider switching it out for. Frozen Mallet is a great all-around item, that little bit of extra health and slow goes a long way. Mid game everyone is usually roaming the map, grouping up, back dooring, whatever. That's exactly what you should be doing with Irelia. Kill any mobs along your path, and be sure to get both blue and red buffs whenever the opportunity arises.
Late game: Warmogs is simply outstanding, almost overkill. With Warmogs, you'll be at 3700+ HP, 4000+ if the game lasts that long. This is an item that you can switch out with situational items if you need. I usually don't worry too much about casters as they go down quickly against Irelia, but if you feel you are being focused too much, get whatever you feel is needed, i.e. Force of Nature, Banshee's Veil, etc.
This is my first guide and I don't have a lot of time to write this atm, but just remember, play smart, don't push too much, back off as soon as you down a tower (situation dependent but is usually smart in any occasion). Try it out, let me know what you think. You might have to play a couple times to get familiar, but this build works 70% of the time, all the time.