Equilibrium Strike gives a very useful low-cost disable allowing you to heavily slow the enemy while doing a large amount of damage. Consider leveling it first to acquire your full ganking potential quickly.
To help your jungler gank your lane, purposefully letting your health drop below your target's can provide a much-needed disable.
In the lane, it can also be used as a harassment tool against champions due to its low cost and low cooldowns.
If coordinated well, it also makes an effective tool for escaping ganks or failed team fights at low health. By clicking the edge of your screen and firing off
a few blades, you can heal off of the enemy champions chasing you to buy time to escape.
Hiten Style is great for jungling and allowing Irelia to sustain herself in lane while also being able to deal true damage to neutral creeps allows her to use other runes rather than armor penetration.
When ganking as Irelia it is important to use your abilities when they will be most effective. If you can engage your target without using Bladesurge then consider saving it in case you need to chase them. Equilibrium Strike can also be of greater use if it is reserved until your target starts to flee, or your health is low enough to leverage the stun to your advantage, rather than for immediate burst damage.
SheenSheen applies itself automatically on Bladesurge, boosting its damage. The manapool increase also allows Irelia to use more Bladesurge to farm and last-hit minions, especially in a lane she cannot control and is forced against the tower.
Buying her Mercury's TreadsMercury's Treads is highly recommended, since the effect works well with her Ionian Fervor, as any tenacity item boosts her CC reduction by up to 41.5/51.25/61% depending on the respectice amount of enemy champions nearby.