Irelia is just as alot of other champions easy to learn but really hard to master. My build is very damn good to start with or get inspired by. I've only played her with this build like four games but with a 100% wins. I really hope you will enjoy my way of Irelia as much as i do!

The skill sequense is a little bit up to you, maxing q as fast as you can is recommended considering its your main farming skill. Make sure you lay an early point in equilbrium strike and hiten style aswell.

The summoner spells depends on yours and the enemies team. Taking flash is what i recommend but i belive ghost works fine too! The ignite is not as important as flash though Irelia is a really good exacutioner thanks to bladesurge.

Pros:
Irelia has great farming.
She is easy to learn.
Great Chasing.
Her laning sustain is pretty good thanks to the heal from Hiten Style and Trancendent Blades.

Cons:
Hard to master.
Farming with Baldesurge can cause mana problems.
Using Trancendent Blades to clear minion waves can ruin an effective damage source during jungle ganks.
Irelia doesn't have a really good escape tool inspite of other characters, thats why i recommend flash.

If you are having trouble last hitting creeps with only basic attacks, Irelia will be a good training for you considering Bladesurge deals more damage than just hitting a basic attack. If you really want to constantly lasthit with Bladesurge make sure you always get the last hit with it, the less you fail the more mana you save (picking up blue buff works really well if can).

Early farming is probably one of the most important things to focus on, especially with my build. Farming with your ultimate is not really what i recommend especially if you have manaproblems or full health.