Some quick notes:

This build is made for solo lanning in 3v3 and lanning with a partner in 5v5.

Irelia is an amazing farmer, specially if solo-lanning, in 3v3 it's your obligation is to last hit every minion.

Depending in your opponent early game, you might want to buy a negatron cloak in your first recall, even before buying boots of speed (thanks to Irelia's very good base movement speed), this way, you will make a quick deal of Kassadins, Luxes, LeBlancs, etc.

Make sure you aim your ultimate not only at your main target, but also to every other champion/minion in sight, since the healing will be much greater, and it will probably save you lots of times.

Why Shappire Crystal in first place? It not only ables you to buy two health pots, but it also duplicates your starting mana, allowing you to abuse Bladesurge for last hitting.

Exhaust is one of the most versatile summoner spells in the game, allowing you to kill, to escape, to disable, etc.
Teleport combined with Irelia's base speed allows you to be everywhere at any time.

Try it, then rate it.