Irelia is by far my favourite champion. Let me explain how to use her and win with her.

Irelia is a butterfly. She is a midgame POWERSPIKE champion and you are WEAK early and fair late. To play her well you need game knowledge to understand both your own powerspikes and your opponent's powerspikes. She has a ton of damage with Hitten Style that never really falls off, as it is true damage. Her W scales incredibly well with attack speed alone allowing you to dish out damage and tank at the same time. The key thing though is to weave Sheen procs into your combos and playstyle.

Play smart, play like a total *****. Just farm and don't initiate trades unless you know they burned a cool down, and even then, usually it's not worth it. Almost always try to have the lane pushing towards you as Irelia controls the lane best this way. Aside from foolish enemies that completely disrespect you, you don't really want to fight anybody early. I like to start mana crystal early for this reason. It nearly doubles your level 1 mana pool allowing you to spam your q more to farm. And you're going to need the mana if you're planning to keep the wave close to your tower, even under your tower. Irelia farms beautifully under tower unless you mess up the reset on one of your Qs. You should feel pretty safe under your turret from dives, even 2v1 against you because of your E.

Depending on how the lane is going, how the mana bar is and how much gold I have I need to make a choice about when to FLIP THE SWITCH. Your first back, you should have a Sheen, especially if you rushed it by starting with a Mana Crystal like I did. Now depending on how painful toplane has been you need to decide what else you need to kill your toplane enemy. If you're losing you might need some defense but usually you want to buy SHEEN (700g)+ DAGGER(300g) + DAGGER(300g) = 1300g HUGE POWERSPIKE

One or two daggers along with a sheen is enough to kill anyone and then some. What you're trying to gage early is whether or not you want to back early and spike off the sheen alone or go for the super spike of also having a dagger or two. Consider your TP situation and weather or not you can tp for a kill with just a sheen or if you want the assurance of dagger(s) or defense.

Much of winning will come down to toplane experience and safe warding and teamwork but all of that aside, Irelia comes down to playing like a ***** until you get a sheen and then flipping the switch. You want to always to pretend like you haven't flipped the switch though for as long as possible to bait them into you. Freeze the waves, punish anyone that blows a crucial cooldown. Look for low life minions to q reset to so that you're close enough to your target to stun them.

Combos:

Little Harass:
Q to a lowlife minion or walk up close enough to stun your target with E. Hit them with your sheen proc and walk away while they're still stunned.

A full Trade:
or walk up close enough to stun your target with E. Unleash your first sheen proc. In the blink of an eye, reassess if you still want to make the full trade, if so activate W, deliver your next sheen proc and then wail on them with W dishing damage and tanking damage with the healing from W. Get yourself someplace safe for when W expires.

A Max Burst Combo w/ Ulti:
Do everything the same as a full trade but use your ultimate to
1) Proc sheen between your autos
2) Create lowlife minions to Q reset to in order to dodge & chase
3) And least importantly aim them at your target to get off the little bit of dmg a ulti shard does.

Tips:
When you decide you need to back, you might consider using your low cooldown ultimate to shove the wave into his turret or take a wave under your opponent's turret. Also consider using your ulti to heal up off a bigger minion wave if you just need to heal up after a bad trade. If your mana is ok and you heal enough you can probably continue laning.

Ward a **** ton and ping like a paranoid person. Ping MIAs not only in your lane but in your allies' field of vision.

Tricks Gifs to be made

I like to take Attack Speed over all else as far as runes are concerned.

I use the pictured Runes page most of the time but I have a few others up my sleeve as well. Note I insist on attack speed on Irelia as it scales her W really hard and she doesn't scale that well with dmg unless she already has good attack speed.

Irelia Default:
29% Attack Speed (Reds & Quints)
216 Health @ Level 18 (Scaling Health Seals)
18 MR @ Lvl 18 (6 x Scaling Magic Resist Glyphs)
4 Flat Magic Resist (3 x Magic Resist Glyphs)

Irelia vs Light AD
29% Attack Speed (Reds & Quints)
15 Armor (Reds & Glyphs)
0.28% Crit Chance (1 Crit Chance Glyph)

Irelia vs AP
20% Attack Speed (Reds and a Quint)
20 Magic Resist (MR Quints and Glyphs)
72 Health (Flat HP Seals)

Irelia vs Heavy AD
20% Attack Speed (Reds and a Quint)
24 Armor (Everything else)

Irelia vs True Dmg
15% Attack Speed (Just Reds)
+124 Health (2 Quints & Yellows)
11 Armor (Blues and a Quint)

You can kinda start with whatever you think will be most useful to you. Sure I like this sheen thing but I sometimes start Cloth Armor, Doran's Blade, Null-Magic mantle and other stuff depending on the matchup and if I took the right runes or if I guessed my lane opponent right. It shouldn't matter too much because Irelia plays like a total ***** early anyways.