Hi all. First I want to tell you that is my first build ever, so all tips will be helpfull for me. Second thing is that english isn't my native language, so please correct me if I will make mistakes.

In this build I'll show you my way to play Irelia. I mainly focus on burst damage early game, slowly changing this to dps late game. If this is way you want to play, WELCOME.

Short overwiev:
Quintessences: Greater Quintessence of Desolation x 3 - you'll do mostly psyhical damage, so armor penetration is what you need.
Marks: Greater Mark of Desolation x 9 - same as Quints
Seals: Greater Seal of Resilience x 9 - for survivability early game, mixed with masteries and doran shield will give you 47 armor total. Not bad i think.
Glyphs: Greater Glyph of Celerity x 9 - for minimalize your ultimate cooldown and let you spam your E ability. If you dont want cooldown, you can take Greater Glyph of Alacrity x 9 - it will let you farm better and heal faster with your W passive.

Offense tree: Masteries for exhaust, attack speed, magic pen and armor pen. You need them all.
Defense tree: Survivability, nothing more.

Short explain of skills usage:

Q - Bladesurge - used for quick dash to enemy, dash out from danger (if enemy unit is on your escape route) or last hit minions.

W - Hiten Style (passive) - is really great for healing on minions waves or when pushing towers. It let you to stay on lane all time, if you play careful.

W - Hiten Style (active) - great when you face opponent, who don't run. If you'll stun opponent, activate this and you can see how fast his health bar is melting.

E - Equilibrium Strike - you will love this skill as much as opponents will hate it. It really saves lives or take it from your foes. If you're low on hp - stun and run. If your teammate is low on hp - slow enemy. If your opponent is so stupid to go without full hp on tower - stun and hit with everything you have.

R - Transcendent Blades - in this build, your ult on last lvl will have 24-28 seconds cooldown - it is ridiculous low cooldown, so you can spam it hard. You have no money and see big group of minions - ult them. Opponent think he can run away - ult him. You're defensing turret, when you have no hp? Ult something to regain hp. If you go 1 vs 1, best choise is to ult your 1st blade, melee hit, ult 2nd, hit, ult 3rd, hit, ult 4th. If opponent is not half hp, he must be Cho Gath.

Skill sequence:
Early game I always take E first and go with my lane partner into our bushes. If someone is careless, I hit him with E and melee hit to die if he's weak, or run, when I'm weaker :) Next skill is Q. It let you to dash to enemy, hit with E and run. Don't spam it, becouse you will run out of mana. Just keep him low, so you can be dominant on lane. Keep in mind, that if you're laning against healer, you must harass him, to force him to leave partner alone. On 3rd lvl I take skill, depending against who I am laning. If there are opponents witout harass ability I'll take most of time E. If they can do some damage to me, I'll take W. Next I maximize E to make my burst damage higer. If E is maxed, you want to go into Q and W in same proportions. Q for lowering cooldown and W for better healing.

Some combos:

Q+E - simple combo for harassing enemy - q, e, run away.
Q+E+W - If you are chasing someone, dash to him with Q, stun or slow with E, activate W and hit, hit, hit.
Q+E+W+R - If you really want to kill - dash, stun, hit, ult, hit, ult.... Spam your Q and E if needed.

Everytime I buy Doran Shield first for hp regen and armor (total 47 armor on 1 lvl). Next I save for Ionian Boots, because I want to have low cooldowns to spam E. Next is Sheen, to make my E damage higher. After this i go for Brutalizer to start doing some melee dmg. Next is Zeal to help farming and fighting. After this is time for Black Cleaver (BF Sword first). When i buy this items most of time game is ended :) If not, I'll buy Yomuu's Ghostblade for extra active attack speed and movement. When you buy it, go into Trinity Force for even more movement and other bonuses. I never played game that I had to buy something more, but you can go in Bloodthirster or some defence, like Banshees Veil, Thornmail, Force of Nature or Guardian Angel.