As good as the Black cleaver now is i suggest its the first thing to build for, as it gives you the health and the right amount of AD in those early game stages. The trinity force after that is for obvious reasons, the tons of damage and those crazy passives that work so good with Irelia. Later on with the Wits end for the big dose of attack speed and magic resist that will stack up. Late games its always good to get a bit tankier explaining the items at last.

When farming, Q is your best friend, killing an enemy with Q gives you back half the mana cost and the cooldown is reset, thats why its important to use it while farming. Even thought your mana can run out fairly quickly while doing that, Irelia has a high mana regen and will quickly regain that mana.

For the marks i have put AD runes because its where you get the most AD from runes (except for the quints) and Irelia needs that AD to be strong, mainly in the early games when maxing Q. For seals i have armor runes because Irelia can be squichy if you play her the wrong way (which lot of people will the first time) and thats why you have armor to help you against those strong early games AD's.
AD runes as glyphs because... Why not!? :)