Hello, (I'm french and my english is little bad, sorry)
My Ezreal is based on the reduction of cooldown, and the full ap.

ionian boots of lucidity and nashor's tooth for 40% cooldown and regen mana is perfect,and the 50% speed attaque of Nashor's tooth is great for last it.

ulti trueshot barrage 48sec cooldown and arcane shift 6,6 sec cooldown nice for escape, mystic shot all the second, and essence flux 5second, it's nice for harass.

Lich Bane Strengthen the Mystic shot which is considered as a basic attack.
void Staff is very important, 40% penetration magic for big dammage with trueshot barrage,
Rylai for slow, and rabadon for amplify the dammage.

movement speed for escape and pursue.

for farm you need the Q in first.

in team fight you can spam the essence flux for the speed attak of your friend and slow the speed attak of the ennemie. You can spam your Mystic shot, arcane shift is good for surprise the ennemie, if you have the controle map you can pursue one ennemie and have the kill.

the Cv is good for see the jungler ennemie and you are never gank, you can too take it for Trueshot barrage. and you can too steal drake/blue/red/nashor with it ( i made all the time ) .
The cv is utility for see your opposant mid, you can follow him if he gank bot/top.