Starting items:

+
Core items:








Focus on getting

first. It will grant you AD and Health, and will make you more durable in your lane.
At next return buy a few more

, and then

.
Now you want to save up to

which will make farming a bit easier, and when you've farmed enough, get

which is a deadly combo with your W.
At this point you might want to upgrade her boots to

for extra Attack Speed or

/

depending on opponent.
Now you would like to finish building

- it grants you more AP and Movement Speed.
At this point you should be careful, and farm as much as you possibly can, because the next item is a

. It is not the most optimal item for Irelia at this point, but its passive is OP and will make chasing champions or getting away easier.
Now we need some damage and critical chance, so the next item is obviously an

.
It will increase the critical damage to 250% and at the same time significantly increase your AD and critical chance.
At last you can either get

or

.