Ionian Fervor
Ionian Fervor (Innate): Reduces the duration of stuns, slows, taunts, fears, snares, and immobilizes for each nearby enemy champion.

* 1 Champion: 10%
* 2 Champions: 25%
* 3 Champions: 40%
* Radius: 800 (estimate)

Bladesurge
Bladesurge (Active): Irelia dashes forward to strike her target, dealing physical damage. This applies on-hit effects. If it kills the target, Bladesurge's cooldown refreshes and refunds 35 mana.

* Range: 650
* Cost: 60 / 65 / 70 / 75 / 80 mana
* Cooldown: 14 / 12 / 10 / 8 / 6 seconds
* Physical Damage: 20 / 50 / 80 / 110 / 140 (+1.0 per attack damage)

Hiten Style
Hiten Style (Passive): Irelia's autoattacks restore health to her.
Hiten Style (Active): Irelia's autoattacks deal additional true damage for 6 seconds.

* Cost: 40 mana
* Cooldown: 15 seconds
* Health Restored: 10 / 14 / 18 / 22 / 26
* True Damage: 15 / 30 / 45 / 60 / 75

Equilibrium Strike
Equilibrium Strike (Active): Irelia pierces her target, dealing magic damage and slowing the target by 60% for few seconds. If the target has a higher health % than Irelia, she stuns the target for the duration instead.

* Cooldown: 8 seconds
* Range: 425
* Cost: 50 / 55 / 60 / 65 / 70 mana
* Magic Damage: 80 / 130 / 180 / 230 / 280 (+0.5 per ability power)
* Duration: 1 / 1.25 / 1.5 / 1.75 / 2 second(s)

Transcendent Blades
Transcendent Blades (Active): Irelia summons 4 spirit blades which she can fling individually to deal physical damage to enemies they pass through, and she heals for 25% of that damage vs champions and 10% vs minions.

* Cost: 100 mana
* Range: 1200
* Cooldown: 60 / 50 / 40 seconds
* Physical Damage Per Blade: 80 / 120 / 160 (+0.5 per ability power) (+0.6 per bonus attack damage)

Teleport / Flash

This is my favourite choice for Irelia. Teleport allows me to shop and return to my lane without missing exp or gold while also being an amazing ganking tool in conjunction with a properly warded map. A well played Irelia with Teleport is very difficult, if not impossible, to push out of her lane on your own.
Note that the Teleport particles can be seen through the fog of war, so use a destination out of the enemy's sight or when he's distracted.

Flash is either great to escape or to catch a running enemy. Irelia can actually cover a great distance with Flash > Bladesurge.

Noteworthy alternatives:

Ghost: Use this if you want to maximize your mobility in teamfights or to get away or catch enemies even better. (especially when running Ghost AND Flash)
Ignite: One should always be in the team. If noone else has it, pick it, even if you have to give up Teleport.
Exhaust: See Ignite, except this is very versatile in it's use. Either to slow down chasers or to shut down AD carries in a teamfight. Btw being Exhaustex does neither lower your attack speed nor the damage from Hiten Style's active part. Awesome, isn't it?