This is just a build I've used after 44+ ranked games with Irelia (she needs a solo lane so if you want to practice her do it in a 5v5 normal with friends or duo with a friend in normals and have him jungle if need be, but Irelia really shines in a solo lane, even 2v1 you can dominate easily). Watch Chaox's videos on how to play her, really helpful and I give him all the credit to how I've gotten so good at her.

Pros:
-Great survivability
-Super tanky when farmed
-Does a ton of damage

Cons:
-Needs to be farmed

These runes are really Simple for why you need it, attack speed and armor pen. Enough said. Armor yellows could also be used along with blue magic resist, but you really need that armor pen so you should keep that. You could also go http://www.mobafire.com/league-of-legends/rune-page-planner#&rune=259:1

You want at least 21 in utility for the extra health regen, buff masteries because you want to have that red longer than 1 minute (or however long it is, very short without the mastery it seems). Flash mastery for obvious reasons, movement masteries to make Irelia even faster (very naturally fast champion, always fastest champion on map probably even faster than Janna).

The reason you get wriggles is to counter champions that kite and harass a lot i.e. Mordekaiser, Singed, and Garen. Irelia needs farm and if someone is constantly harassing her to where she can't get out there and farm it's a problem. Even if they don't harass you should still get it because if you have wriggles and they don't have it or any other type of survivability you can nonstop harass them without them being able to attack you. Wriggles resolves that problem with the life steal and armor, the damage is just an added bonus to the mix. For added survivability always get a philo stone after you've rushed your wriggles, that way you'll never ever ever ever have to leave your lane.

Don't always get your Q first, it's not always needed. Wait till you see if they're invading your jungle, if they are grab your e (for obvious). If they aren't just stick with your Q. W is also acceptable if you're going against someone who didn't grab boots or is just plain slower than you and you want to harass. Always max your W first, always. There should never be a time where you don't max your w first. Your w is your survivability in your lane up until you get your wriggles or philo stone and your damage. It does true damage to so if you're going up against a Singed who has armor runes, you can still do massive amounts of damage to him. Max your E second, then your Q. You want to max your E second for the cooldown reduction, having your E up every couple of seconds is very nice. You can max your Q second if you are dominating your lane and just want to hit them even harder, that is definitely plausible as well.

Flash isn't a must have but it's probably the best summoner spell. Ghost is also ok in its place but she doesn't have any escapes so I would say get it.

Exhaust, Ignite, or Teleport are all ok in this place. Look at their team to decide. Get exhaust if you think it's someone you're just not going to be able to handle so you can escape/make them do less damage. Ignite if you want to have that for sure kill. Teleport if you want to stay in your lane forever (what i usually take, Irelia really needs to farm to be good and having teleport will make sure you get your farm).

Farm it up. In team fights you're the one that's going to be taking a lot of damage and dealing a lot of it out because you're the one jumping on the squishies. Always jump on the squishies, if you're attacking a tank with a squishy behind him/her (Leona doesn't really get any play in ranked anyways) then you're doing something wrong.

Irelia as a jungle is alright obviously you're not going to get as much farm if you jungle but she has nasty ganks cause of her damage output. I would suggest just laning with her.

Always take your team's red. Always. Your team will thank you.

In team fights you always want to jump on the squishies as I've explained above. If you have teleport and mid/bot lane is getting killed teleport in there and help them out (as long as the enemies are at least at half health and your teammates can help you out a little).

Irelia needs it. If you don't have 200+ by the end of the game (even if they surrender at 20 you should at least have 150+) you need more practice at her.

I know this guide is just a basis for people to kind of know what to build, etc. and not really how to play her so after reading this guide i implore you to watch Chaox's videos on how to play irelia at this link http://www.solomid.net/guides.php?g=720