Irelia is free to play this week [December 29th, 2011], so I decided to make this short guide on how to play her a multitude of different ways. I am not making this guide so you follow it to the letter, I am only posting it to help you better understand the champion so you can make educated decisions on how to play her in various game situations.

Pros:
Is not affected very much by CC effects [With Merc Treds].
Does a good amount of damage even if she is built more like a tank.
Her Q can go through walls if an enemy is within range.
Her Hiten Style and Transcendent Blades give her automatic heals.
Can do true damage with Hiten Style

Cons:
Mana Dependent Early On.
No method of escape.
Her Ult is a skillshot, so you have to lead or predict your opponents' movements.

I find Irelia is best played with a tank mastery tree of 9/21/0 focusing on Armor Pen and Health. The extra HP allows you to solo top in a 1v1 or 2v1 if you have jungler. The Armor pen is nice to have when your opponents attack your tower because you can Q into them and auto, combine this with Sheen and they will back off slightly. I like this mastery set up most of all with Irelia because it allows her to take a lot of damage while also giving out a lot of damage.

You may also choose to build Irelia as a more AD oriented champion, in which case you will have less sustain and more damage. [21/6/3] This build is also viable for Irelia. The extra armor pen will make you even more threatening than the 9/21/0 build. The life steal will also allow you to stay in lane longer, especially when you combine it with Hiten Style.

Greater Mark of Desolation Are my number one choice for reds. They help you cut right through your opponents' low early game armor. Combine these with your Armor Pen Quints and 9/21/0 Mastery Page and you're going to be doing quite a bit of damage.

Greater Seal of Armor These should be your number one pick for yellows because Irelia's base armor is only 15. You will gain 3.75 armor per level, but even with this nice boost per level, Irelia will not be able to dash in to farm if her armor is at or under 20 for the first 3 levels.

Greater Seal of Replenishment For those who find themselves running out of mana early game, I recommend these as an alternative, but only in conjunction with a few Greater Seal of Armor. Note: If your mana is running very low with Irelia early game, you do not know how to manag

Greater Glyph of Vitality I put these on Irelia because I like the extra HP.
Greater Glyph of Scaling Magic Resist would be a nice choice because your Magic Defense increases at a decent rate of 1.25 per level
Greater Glyph of Magic Resist These are nice for an immediate boost to Magic Defense if you're the type of person who likes to really get aggressive early game, but don't want to get rubbed out when you start to poke at opponents.

To be honest, you can use what you wish as far as blues go. I see many people use completely different runes, but still get great success. I know these rune options are not as liberal as I stated they would be in the introduction, but facts are facts. If you want to do enough damage to entice your opponents to acknowledge you in a fight, you need Armor Pen. If you don't wish to die a lot in lane, you need Armor. But blues are up for grabs.

I think it would be best to talk about skills before items so you can better understand why certain items apply to Irelia, while others do not.

Boots:

Mercury's Treads These would be my first option for boots because they add onto your passive and increase your relatively low Magic Defense.

Berserker's Greaves Are not recommended. They increase your attack speed, which means the only skill you can benefit from is your Hiten Style. These would be good if they were coupled with a Phantom Dancer and Infinity Edge, but neither of these items is really required for Irelia to do well in a game.

Mobility Boots These make you super fast. Great for ganking mid or for catching up to team fights. Her passive does giver her some tenacity, but nothing in comparison to a set of Mercury's Treads. If you want to move quickly, you can get these, but think about combining them with another tenacity item, such as elesia's miracle.

Ninja Tabi Even though dodge runes have left us, these are still quite viable. A 12% dodge rate will be very helpful when dealing with those heavy AD with high crit rates and attack speeds such as Tryndamere and Master Yi. The extra armor really is not needed on her.

Ionian Boots of Lucidity Irelia does not need to spam her spells in order to be effective. Considering she has fairly low cool downs at level 18, I find these boots to be a little redundant.

Attack Items:

Hextech Gunblade Is an interesting option for those who want that hybrid Irelia. It will give you spellvamp and life steal, so you will be much harder to kill. The unique active allows you to slow down fleeing opponents, which allows you to get in range to use your Q. Overall, this is a good item for most Irelia builds.

Bloodthirster I like this item because it works very well with Sheen. Gives a nice chunk of damage and life steal, makes you much harder to kill.

Sheen Will increase your total damage after using skills. This is an excellent item to use in conjunction with your Q. Also builds into Trinity Force.

Trinity Force Overall a perfect fit for Irelia. She gets every bonus from it. I usually just get Sheen in games, but will build into this if I need to.

Phage Nice for slowing down your opponents, makes your more tanky, gives you a little AD. Also builds into Trinity Force

vamperic scepter This will give you more sustain in lane, especially when combined with Sheen and Hiten Style.

The Brutalizer Gives you a little bit of armor pen. I wouldn't recommend this item unless you already have a fair amount of armor pen in your masteries and runes.

Last Whisper Good item to have if your opponents' are building lots of Armor.

Black Cleaver Not an item I usually get for Irelia, but it is very helpful for your team in taking down opponents with lots of armor. Because it stacks so high, this will also go well with your armor pen masteries and runes.

Defensive Items:

[Warmog's armor]] This is just amazing for Irelia because it allows you to take so many extra hits from your opponents. Considering your passive reduces opponents' CC, you can absorb those CCs and give your team an edge in team fights. You don't want to buy this late in game because you'll need to farm it up.

Eleisa's Miracle This item will allow you to have 45 tenacity with your passive [75 tenacity with 3 opponents in range] It also helps you out with your HP and MP regen. It's funny when the enemy Sion says "dude you're hacking, my stun isn't doing anything to you." Also allows for Mobility Boots

philosopher's stone This builds into Elesias Miracle and will give you some HP, some regen, and 1 gold every 2 seconds.

Guardian Angel Brings you back to life and buffs all your defenses. Nice buy for 2.6k

Quicksilver Sash and Banshee's Veil are useless. You have your passive and 1 tenacity item to compensate for the lack of these two items. I know they look cool, but they are not needed for Irelia.

Negatron Cloak This is a nice buy for only 700+. Gives about 50 Magic Defense, which will put you over that 100 marker. I don't build into Force of Nature form this item because it gives enough magic defense on its own, and warmong's armor will make it seem as if AP nukes are like regular auto attacks.

Thornmail Combine it with warmong's armor and a Negatron Cloak and you can watch your opponents kill themselves (maybe). It's a bit excessive considering you'll have a fair amount of Armor in late game, but if you're dealing with AD heavy opponents, get it.

Ionian Fervor Is Irelia's passive. I'm sure you know what it does, but I would like to point out that this is not detection skill like Morgana's Soul Shackles. You will not see "40% tenacity" appear on your screen if 3 enemies are in the bush right next to you. So don't rely on it to get you out of ganks.

Bladesurge Is your farming tool early game. You want to last hit minions with this up till level 3/4. By then you should be able to last hit minions with auto attacks. Note: This skill has a 1:1 AD ratio, meaning if you have 1000 AD, this skill will deal 1000 bonus damage. It also allows you to go through walls if enemies are target-able on the other side, and it will reset if it lands a killing blow. Because of this, you can Q into a minion, killing it, and then Q into an opponent next to that minion! This is a tactic used to get super close to opponents, and most people do not know Irelia can do this, so take advantage and practice it!

Hiten Style Passive will heal you based on level and the active will deal true damage. This is a must have if you are soloing top against 2 people. Note that you don't want to go full throttle on attack speed to use this item's active.

At maximum level it only does 75 true damage, so even if your attack speed was 2.000 and you hit your opponents for the full duration of the skill, you would only do about 900 true damage. Getting Sheen and some AD items will enable you to do more damage with your Bladesurge and Equilibrium Strike than if you sat there getting beat up for 6 seconds auto attacking, and then waiting for the skill to reset.

Equilibrium Strike This is Irelia's "nuke" skill. It's not the most reliable skill because it can stun or slow depending on your hp vs your opponent's hp. I recommend leading in with Bladesurge and then popping Equilibrium Strike to stun. This gives you time for Bladesurge to come off of CD, and lets you get in some free hits with your Hiten Style.

Transcendent Blades This is your other built in heal skill next to Hiten Style. It works best for clearing creep waves or for team fights. I find a lot of people miss the skill shots with this one quite frequently.

I have found the best way to use this is when opponents are chasing you. Just click a point on your mini map, and while opponents are chasing you throw your ult at them. This will cause them to run right into it, and give you health. If you manage to hit your opponent all 4 times, you might have enough HP to actually counter him and get a kill. This is also nice to pop late in a 1v1 when your opponent thinks he can out last you.

You have to remember that when you play Irelia you have the ability to start fights. Your passive will allow you to take away a lot of the opponents' CCs, allowing your team to crush them.

Remember you can always get to opponents behind creep waves by using Bladesurge to kill a minion close to an opponent, and then using it again to attack that opponent.

Irelia can be built however you want, but I recommend a tanky AD over a straight AP/ AD/ Hybrid. You'll be able to take more damage, and give more out.

I didn't list all the items which can be applied to Irelia, but I did list a good 90% of them. If you want to know about different item choices then I suggest trying them out for yourself. Remember the items list was only a suggestion and a reference, I don't want anyone to follow it word for word.

Regrowth Pendant and an MP potion. I get about 1.6k and come back to base for boots and Sheen. Next I save up another 1.6k and come back for B. F. Sword. Then I get Giant's Belt. Usually games end before I can go too much farther into my build other than warmong's and bloodthirster and merc treads. I like to get the pieces for my big items before I actually buy them.

ie: if I have 1.3k, a B. F. Sword and a vamperic scepter I will get Sheen instead of Bloodthirster because the effect of Sheen will allow me to do more than if I had Bloodthirster and I have enough AD and life steal from the two components of the Bloodthirster to get me through most situations.

I hope my guide helped you, and see you in game.