AP ez is a bursty mage who relies on good positioning to get his combo off (E W Q). He is a hit and run champ who due to his lack of health should never hang around aftr landing his combo as retaliation will really hurt.

Pro:
Great burst
Underestimated dmg
Excellent escape mechanic
Global Ulti

Con:
Squishy
Quite item dependant
Escape mechanic is mostly used to gain good positioning for combo.
All skill shot based.

I run Ez with Magic pen reds, mana per 5sec yellows, flat CDR blues and flat AP quints. These runes give a decent amount of dmg at the lower levels with the extra 15ap and the mana regen gives good lane sustainability especially with a meki as first item and finally the magic pen runes are great for obvious reasons. With Ap ez as long as you are running caster runes there is nothing wrong but CDR is highly recommended.

Masteries are pretty self explanatory 9/0/21.

For items you can replace a morellos with a death fire grasp if u please so you can add a bit more dmg to your combo. The core items are Ionian Boots of Lucidity Lich Bane Morelle's Evil Tome. After this its really up to you, build the final items at your own discretion and if you are doing well feel free to grab a majai's Soulstealer and even a Sword of the Occult and a laviathan if you a feeling cocky.

Max Essence Flux and Arcane Shift first with a point in Mystic Shot (as when it lands on a enemy it lowers your cool downs by 1sec and grab) Trueshot Barrage when ever possible.

I run Ghost and Teleport but if you like you can take Flash as a Arcane Shift Flash will get you out of most sticky situations.

Ez is a pretty poor farmer and he most effective way is to last hit with auto attacks and your Q, once level 6 is reached its ok to farm and harras with your ulti due to its low cooldown, i would,n't recommend this though because your ulti is better used to clear pushing creep waves at far away towers and sniping off low champs.

Ez is not the most powerful champion but there is no reason why you wouldn't play him. This build turns Ezreal into a burst mage so don't take him as a 5th pick when your need a jungler. As always talk to your team make sure they know who your going to play and what build you are going.