Hey fellas, Lionelo here, from EUNE.
My ELO in season 2 was about 1525, Rising and falling depending on if my duo partner was online(duo = 100% win since I don't have to rely on luck not to have ap tryndameres on my team...).
I main Irelia as my top player, because she is simply the best one out there. Cut her down early, she destroys you late game. Feed her, and you won't get to late game.
Why is Irelia so OP? In my opinion, her ability to build herself as a tanky champion and rely on Attack speed items, and of course Trinity force's valuable stats as her source of damage is what makes her so strong. Aside from that, she is basically a leech. If you won't focus her, she just sticks to your Carries like an actual leech.
Side note - If you don't plan on taking risks, such as hiding in a brush with less than 5% HP while fleeing from a vayne, and simply insta-killing her when she comes in it before she has a chance to react, instead of fleeing for your life.
As an Irelia player, I look at every situation as if it was Life or Death. If I see Life, even just staying alive with 10 health, I go all in. Otherwise, I play safely.

Here is a list of things you need to look at when you play Irelia:
1. You need vision, constant vision. Always carry a couple of wards on your way back. Ward enemy lane brush, ward the tribush, ward the riven brush, ward every where you need to grant yourself vision.
2. Farming - If you don't play on last hitting all game long - Don't play Irelia. Irelia has very expensive builds, and if you won't farm your money, you won't be able to last till late game, because Irelia is driven by her items.
3. Builds - If you want to do well, you need to build your Irelia to counter enemy team. The builds I gave are just an example. In the Item section below i'll explain more about how to build.

Oh and one more thing -
4. GUTS. LOTS AND LOTS OF GUYS. If you're a *****, then don't play, unless you can do what the wise PhantomL0rd once said, Grow a pair, grow a pair of two hairy balls! (Yes, that was a motivational speech he said to a girl he was tutoring. This guy is indeed a genius.)

To be a successful Irelia, you need to know how to build to counter the enemy team.
The builds above are just a couple of examples.

Here is an Item Pool to choose from when you play, according to your situation:

Offense - Zephyr, Blade of the ruined king, Bloodthirster, Trinity Force, Statikk Shiv, Ravenous Hydra and Youmuu's Ghostblade.

Defensive - Warmog's Armor, Frozen Heart, Banshee's Veil, Iceborn Gauntlet, Spirit Visage and Runic Bulwark, Randuin's Omen and Ohmwrecker.

Hybrid(Off+Def) - Wit's End, Mercurial Scimitar, Maw of Malmortius, Atma's Impaler.

Utility - Shurelia's Reverie, Executioners Calling(In case of no Ignite and you are facing a strong sustain champion).

Boots - Mercury Treads(In case you get them, do not buy Zephyr), Ninja Tabi and Berserker Greaves (Must get Zephyr if you get then).

Why suddenly Berserker greaves? If you're facing an easy lane, you don't need the tabi to survive, or you don't need the magic resist from Merc Treads and you bought Zephyr, Why get something else when you can get a bit of extra attack speed for you W active? I say - Why not.

Enchantments - I would say either Furor for a bit of aggression, or Alacrity for the sustained speed.

So here, it goes down to a couple of choices:

Marks - Attack speed / Attack Damage : It all comes down to play style. I would prefer to get 5 Attack Speed and 4 AD if I get the attack damage from the offense tree in the masteries, but otherwise I would use 9 Attack damage for the easier early game last hitting.

Seals - Armor. Only armor, in All cases.

Glyphs - If you're facing a magic damage dealing champion(Shyvana\Vlad\Rumble\W.E) get flat magic resist runes. Otherwise get scaling magic resist runes.

Quints - Attack Speed / Attack damage / Movement speed / Flat Health - Quints is where it comes to flat down to what you prefer. Personally, I use Movement speed quints. Especially now when movement speed is more effective(Base speed raised by 25 for all champs), This bonus movements speed in just invaluable early game. Eases fleeing, chasing, and moving back to lane / out of lane. I just love the bonus movement speed period. Get AD for easier last hitting, AS for the dueling potential with Hiten Style, and Flat HP if you like the early beefiness you get from it early in the game(this + Masteries = more then 100 extra base health LEVEL ONE!).

So anyway guys, I hope you liked the guide. Since my computer is currently a **** and I can't play lol for some time, I can't get you photos to explain stuff. I'll add more sections later.

Good luck and own dem *****es in the field of injustice(how can there be justice when Irelia is so op?) ;)