I'm guessing attack speed is important on her to get the most out of w
You bet. Don't be afraid of getting some AD though. The biggest thing to know is that she isn't someone you want initiating. You want to play her like an assassin going in from the side and taking out the carries. Personally I like to get Zephyr for her first major item. She can use each of those stats really well and lets you get some ninja tabi or other boots. (the tenacity stacks with her passive and the mastery)
General rule is that after 3 points of W, you'll be able to out trade near anyone in a simple fight. You may have kill potential at that point. nd then again at 6 with your Ulti.
This guy gave good advice.
Level 5 irelia is really strong compared to other top laners, and in a lot of cases has REALLY strong kill potential at this point.
Now is often a good chance to all in your enemy (of course it depends on your health, mana, and lane position and such) and come on top with a kill. Q to a minion to refresh it and get in range, auto attack and E for damage, and Q for a last burst of damage before W wears off, if they are running and get out of range, or for the kill.
Irelia is pretty simple to build so im going to assume you are good in that aspect. Attack speed (usually botrk, triforce, witsend), tankiness (always situational - randuins, warmogs, SV, etc), and something to slow targets (botrk, phage,FM) are always good pick ups.
Irelia is pretty assassin'y, so her biggest kill potential range is between levels 5-11ish when you have big damage item. Its usually a good idea to roam or force team fights at this point, because you will do A LOT of damage to squishies.
Remember, If at first you don't succeed, you fail...