-First to say, my favorite champion is Ezreal and I really wanna help you guys with he's building.
-Q / Mystic Shot it's his main damage dealer in the early and mid game ('cause in his late game he is based more on normal attacks).Every time you want to shot it/use it you must position yourself if not you are going to have a bad time!After you positioned yourself you must hit a enemy or even a minion(never waste you Q, it's important).Do not use your Q only for farming,save it for harassment.
-W / Essence Flux it's a good way to help your teammates in team fights and doing Baron or Dragon.In my opinion it's not a good skill for killing, it's just for giving you an advantage against the enemy Ad Carry!
-E / Arcane Shift 3 words for you my sir: Positioning in Fights!. This skill it's a very good way to position yourself, running from fights(that you lose) and running for the kills. Oh and never ever use this skill to attack in a bush or to go very close to an enemy( i mean like VERY CLOSE : ezreal->||<-enemy )
-R / Trueshot Barrage a very powerfull ulti that you must use it for: -Starting a team fight -Getting a kill from far(sometimes from the base) and -Clearing minions from far away!. Use it wisely when you snipe.

Careful Ezreal
This build is for those who play Ezreal as a careful Ad carry, ready for ganks and for team fight.You have a good amount of Health so don't be afraid of your enemy, just position and kill(my moto).

Early Game
1.Play carefully
2.Harass with Q the enemy Ad carry
3.Watch out for minions with low health
4.After level 3 try to be aggressive if the enemy Ad carry is at half of his health!
5.Watch out for ganks and don't blame you support if you die.

Mid Game
1.If you lanes works good and you destroyed the first turret try ganking(with you supp) the mid lane or help your jungler with the Dragon
2.Don't forget about the farming and ask your jungler for Red Buff
3.Push your lane So that you don't have problems
4.Snipe with your Ulti low health enemies
5.Be nice with your supp

Late Game
1.After getting your Phantom Dancer try to harass with Basic Attacks
2.Always hit something with the Q so that you increase you attack speed
3.After completing the build you are a killer machine that doesn't die very fast
4.Your ulti is great for killing the enemy Ad Carry and his Supp
5.If you win/lose don't forget to thank you supp

Pros
-very good mid/late game
-hard to kill in mid/late game
-Doesn't die quick(if played good)
in early game
-good mobility and helpful for team

Cons
-squishy in early game
-can lose lane very fast
-mana eater in early game
-Essence Flux/ W is not good for Ad build

Aggressive Ezreal
This is the Aggressive Ad carry build.Killing machine from early game but squishy even in late game so i recommend it for those who know how to play Ezreal.

Early Game
1.Harass with Q both enemy laners
2.Watch out for ganks('cause you are squishy)
3.After level 3 Go harass with combo Q-E-Q-D (chose the lowest health enemy)
4.Use E / Arcane Shift for escaping from ganks(don't use it to much because it's a mana eater)
5.Enter in fight only with your support

Mid Game
1.If lane works good help the other lanes
2.Snipe with ulti
3.Spam you Q / Mystic Shot (sometimes you can even kill a enemy you didn't want to shot!
4.you are still squishy so stick with your supp
5.In team fight, don't forget to position yourself (it's important so you will not die first/quick)

Late Game
1.You become a squishy killing machine(sometimes you can kill the enemy Ad carry wit 2 or 3 basic attacks)
2.Ulti good for team fight and sniping
3.Stick with your supp
4.Focus the enemy Ad Carry( make 1v1 one lanes and try to win)
5.Use your mobility very careful (you have Flash and E so you can escape really quick)

Pros
-killing machine
-good for stealing Dragon/Baron
-Q damage is high as f**k

Cons
-very squishy
-easy to be gank in early game
-mana eater in early/mid game