With the summoner spells you can take whatever you want there is no real reason I put flash exhaust; personally I use flash teleport myself so I can shop, heal and not loose too much exp or minion kills.

The masteries are pretty standard, being tanky is an important part of this build, I've tried to max the amount of armour at the start because I play solo top where most of the time your opponent is going to be an ad bruiser, however you will start with a low amount of magic resist so be cautious when fighting against AP users.

I take a point early in "Bladesurge" for last hitting minions, then one in "Equilibrium Strike" for the stun which will help you escape if a fight goes bad or escape an early gank, then max "Hiten Style" as your main source of damage, taking your ultimate whenever it is available, I max "Equilibrium Strike" second for the stun duration and "Bladesurge" last and I'll explain later that not having the damage on blade surge can be an advantage.

Armour pen reds (speaks for it's self) flat Armour yellows (maxing armor as I explained earlier) Magic resist per level Blues (you probably wont see an AP user for a while) and Flat Health Quintessences (for early game survivability)

I take Doran's Shield first but take what ever you feel comfortable with, then "Avarice Blade" for the extra gold and I turn it into a "Youmuu's Ghostblade" later, then "Mercury's Treads" because combined with your passive nothing will be able to stop you, then I start building "Trinity Force" because all the elements of this item work well with Irelia giving her a lot of damage; I start with "Phage" for the health to help her survivability but you should build it however it works best for you, next item is "Guardian Angel" makes you tankyer, then "Maw of Malmortius" I'll explain this one later, then "Madred's Bloodrazor" it will make you a bit tankyer the attack speed works well with "Hiten Style" and will help you kill tanks and bruisers, and last of all "Youmuu's Ghostblade" this will help you chase people down and the attack speed works well with "Hiten Style"

Irelia's abilities make her more suited to fighting people who have a higher percentage of health than her and my build is make to optimise this with the items "Maw of Malmortius" and "Guardian Angel" so when you are full health and your opponent is full health you should "Bladesurge" on to your opponent (hopefully they wont run away; and having less damage on your "Bladesurge" will increase the chance that they will stick around) and auto attack for a while until your percentage health is lower than theirs, (the lower you let your health drop the better because of "Maw of Malmortius's" passive) then use "Equilibrium Strike" for the stun and activate "Hiten Style" and "Youmuu's Ghostblade" this should drop their health very quickly they will most likely turn and run at this point but the speed from your "Youmuu's Ghostblade" will help you keep up with them as you should have gotten almost 4 hits to increase its duration also your "Trinity Force" will be slowing them, now your can use your ultimate as they run away to easily hit them and if they start to swerve to dodge it this will cause them to slow down and allow you to catch up and if they start to get away you can use "Bladesurge" into a "Equilibrium Strike" to slow them down.