Irelia is a melee assasin, played as a full damage dealer of as an off-tank.

Passtive:- Ionian Fervor
Reduces the duration of stuns, slows, taunts, fears, snares, immobilizes, blinds and silences for each nearby enemy champion. ■1 champion: 10%
■2 champions: 25%
■3 champions: 40%
■Radius: 1200 (sight range)

Abilties

Blade Surge - Irelia dashes to target enemy or champion dealing phycical damage. If irelia kills the target, the ability comes stright off colldown and refunds around 35 mana.
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 - Passivly Irelia restores health from each basic attack. Upon active irelia deals True Damage to the target and doubles the amount of life steal.
Health Restored Passive: 5 / 7 / 9 / 11 / 13
True Damage: 15 / 30 / 45 / 60 / 75
Health Restored while active: 10 / 14 / 18 / 22 / 26

Equilibrium Strike- Irelia deals Magic Damage slowing the target. If the enemy has a higher amount of health than Irelia, the target is stunned instead.
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- This is Irelia's Ultimate, she summons 4 blades and fires them one at a time in the direction your cursor is. Health is also restored when the blades hit.
Cooldown: 70 / 60 / 50 seconds
Physical Damage Per Blade: 80 / 120 / 160 (+0.5 per ability power) (+0.6 per bonus attack damage)
Maximum Physical Damage to one target: 320 / 480 / 640 (+2.0 per ability power) (+2.4 per bonus attack damage)

If against a champion like riven, renekton or xin etc....I'd recommend start with Cloth Armor first and 5 health potions.

Grab Mecery Trends or Ninja Tabi depending on the damage your oppoinent is dealing.

Start rushing into trinity force as your first complete item, starting with Phage.
If mana is becoming an issue, then begin with sheen instead.

If you so happen to be up against a teemo or any other ap champion, an earlly Hexdrinker will make you more defensive as well as keeping the damage.

Guardian Angel is your next item, this will give you armor and magic resist you'll need to still remain tanky and survuve longer in team fights...........if you are getting focused with that, then they're idiots XD....................Building a heart of Gold Before hand may increase the time in which you purchase Guardian Angel due to the extra gold.

After that, i'd start to consider building some health, whilst still keeping the armor and magic resist.
Randuins Omen is a good item to have on any tank, slows the attack and movement speed of any champion e.g. ad carries.

Banshee's veil as your magic resist item. I'd recomend this over force of nature since you get the extra health and cannot be disabled if the sheild is up. Force of Nature still a good item for against those hardcore ap champs.

So you have your attack, health and defence, now some attacking speed.
I have been using Ionic Spark as my attack speed item. Wits End is all well and good too if you want to remain tanky, but Ionic Spark will deal more Magic Damage after a few basic attacks and you'll be much faster.

Pros:

Makes a good off-tank
Very good at farming
Plenty of durabity e.g. Life Steal and health Regen
Deals True Damage
Excells well with attack speed and health items
Makes a Great Solo laner and can also Jungle
Very Strong Mid and Late Game
Good at sticking to single Targets

Cons

Uses alot of Mana earlly game
Can't really do much at earlly levels
Dose not work well when duo lanning
A little squishy
Weak against tanky champions