Irelia is a melee AD off tank with alot of damage. You really want attack speed on Irelia because her W deals 75 true damage at level 9. So you want Survivalbility and Attack speed on her.

I recommend magic resist per level blues, because you will get a nice ammount of magic resist + your items when teamfights starting.
Armor yellow for the survivalbility at top lane.
Attack damage reds because you need attack dmg, with my build you will get about 2.000 attack speed anyways.
Health Quints, it will give you early lead in beggining and can help you alot.

Pretty offensive mastery tree, Armor and bonus health in defence, and attack speed , attack damage and some armor penetration.

This items are perfect for Irelia, gives her hell off a attack speed and alot of armor and magic resist, and much health. She can charge in use her combo and take alot of damage, + guardian angel is very needed for her!

Maxing W gives you alot of early bonus damage vs almost any top laner. Bonus 75 damage in lvl 9 is alot, giving you a nice lead.

Good spells for Irelia is Flash + Ignite.
2 other good spells for irelia is Exhaust + Teleport, considering their pick.

Irelia is in desperate need of farming. So try farm as much as possible to build up your late game potential. Your ultimate has a short cd so use it on minions, it also heals you if you need health.