Ok, so this is my first build. Constructive criticism is, of course, welcome. Being a d-bag is not. Irelia is a great melee DPS champion. She has a slow/stun, true damage, and two ways to heal from abilities. She also has reduced CC from her passive, which makes her great against carries, which often carry CC. While that strategy is primarily what this build focuses on, Irelia is also great against tanks, combining attack speed with true damage, which is devastating to high hit point targets.

In case it doesn't show the screenshot, the scores from 5 consecutive games are as follows (all wins):
7/6/11
27/4/8
14/7/11
13/7/10
10/8/10

My runes are my standard melee DPS runes. The armor pen is great for Irelia because half of her abilities cause physical damage. Dodge runes are also great for that little extra survivability. Cooldown reduction allows her to spam abilities. At full CDR, her ultimate has less that 25 seconds of cooldown. While I do not include and CDR in this build, you can adjust it situationally to include it if you like. Also, this makes mana buff a great thing for Irelia to have, and you should grab it, as well as lizard, as often as possible. Flat health quints provide for extra survivability during the crucial early game, allowing you to score some early kills.

Masteries are my standard 21/0/9 for melee DPS. The extra attack speed and magic pen give her some extra damage the whole game and makes her all the more deadly.

I take Bladesurge first, as that is my main harassing ability. I then take one point each in Equilibrium Strike, and Hiten style. I max Bladesurge first, as I use it often when harassing, then Equilibrium strike. I get one point in Hiten Style to help stay in the lane longer, but max it last. Of course, take levels of your ult whenever possible. As far as using skills, if you are just harrasing, then a Q-E combo while suffice nicely. You do need to be careful though, as she does not have a way to get out except for running, so do not harass if they can trap you. If you are going into a fight, intent on a kill, then W-Q-E is the way to go. Your Q procts all on-hit effect, including the hiten style true damage. Her ultimate is what prevents many people from mastering Irelia. Her ult is a 4 hit skill shot, each shot having to be triggered manually. Her blades fly toward wherever the cursor is. Because of the relatively low cooldown, this ability can be used pretty often. It can be used to wipe out minion waves, restoring massive amounts of health if aimed to hit as many minions as possible. It can also be used to finish off fleeing champions, as its range is really good. It can also be used to save your life if you are about to die. Main point about Irelia's ult: you can use it while running and she won't stop. This makes it ideal for fleeing or chasing. Master this skill, and you will get kills and will survive much more easily.

I chose flash and exhaust for my summoner spells. Irelia has no natural escape mechanism, so flash allows me to escape sticky situations. I typically use exhaust for chasing, but sometimes, I will use it to weaken enemy effects to allow me to survive if I am being chased myself. This allows you to turn a potentially deadly fight into a kill.

As always, items should be situational to your particular game. This is the build I use most often, but no build is set in stone. I start with a phage, for the damage, health, and slow, allowing me to chase and kill early on. After that, I get berserker's greaves, which give extra attack speed. Attack speed is great for Irelia, because it feeds her Hiten style, which can quickly get health back with the passive, or work down high hitpoint tanks with the active. After boots, I complete out Trinity Force, usually getting sheen before zeal. I go next with a Stark's Fervor, for additional health regen in battle or laning. At this point, Irelia has good movement, attack, and decent crit, but not a huge amount of damage, so I go for an Infinity Edge. Attack speed works very well with critical chance, because the more often you hit, the more often you get a critical strike. This may seem obvious, but a lot of people prefer to stack huge damage with fewer crits. With Irelia, more hits is better, because you get more crits, and it also procts Hiten style. Speaking of attack speed, it is at this point that I get phantom dancer. This further increases attack, crit, and movement speed. You should be able to easily move about the map, setting up ganks or defending turrets. I often finish out with a madred's bloodrazer. While the extra attack speed is nice, I primarily get it for the extra damage and the passive. This allows Irelia to be a true threat to any member of the enemy team. Depending on how the enemy team's tanks are building, I often move this up further into my item build, building it earlier.

In conclusion, Irelia is a bit tricky to pick up on, but used properly, can carry your team to victory. The most difficult thing is learning her ult, but that will make or break you with Irelia. Feel free to comment with your success stories or suggestions! Hope you enjoyed this guide and happy hunting!