Passive: Ionian Fervor
This stacks with the defensive mastery Tenacious and with Zephyr's tenacity making Irelia almost immune to CC's in a teamfight. Also when you get ganked, it is much easier to escape from the enemy's stuns.
Try to not rely on this ability to last hit unless you're at tower. This ability will consume a lot of mana even if you are getting last hits. Use it as a last resort. There is no need to lose 30 mana to get a last hit if you're able to get it through basic autos. This is a very useful ability to farm at turret. At level 2, you are able to get every single CS at your turret, even if you aren't able to auto all the range minions once, because you can let the turret hit the minion, then auto+Q.
TL;DR: Conserve your mana, and you shouldn't miss any minion kills.
Very important detail: When fighting or harassing, your Q will proc your W when it is activated. Always wait for your W to be up to Q the enemy, as you will do a lot more true damage.
W: Hiten Style
One of the strongest abilities in the game. Gives you decent sustain and allows you to 1v1 almost any champion by level 9. 75 true damage per hit along with proccing on your Q allows for almost 750+ true damage in a one on one trade. Always activate this ability when trading hits.
E: Equilibrium Strike
A very strong skill for a bruiser. It will stun the enemy if he has higher % or equal % health than you (This means if you're both full health it will stun), otherwise it slows. When the enemy jumps on you, wait until you fall below their % health so that you can stun, rather than trying to slow to get away. When engaging, try your best to stun rather than slow. This could involve Qing the creep next to them so you don't bring their health below yours or even flashing next to them if you know they'll die.
R: Transcendent Blades
This ability actually does a lot more damage than you would think. Don't recklessly farm with it, but it isn't a bad idea to ult a wave in order to secure dragon or to invade the enemies jungle. Also it's a great sustain ability against a huge wave of minions. You can even stop recalls with it to keep the enemy at his turret for ganks. Overall, it's a pretty good ultimate, but also it's Irelia's only way to do AoE damage to push a lane, so you need to find a good balance..