Ezreal is a aggressive adc which needs an aggresive player,if you're passive player do not look at my guide it wont end well for you.
Ezreal gets countered by Graves&Draven
You can manage to beat graves&draven only when your jungler ganks there's no way that you'll beat 2 of them alone.
Another annoying one is Ashe her pokes are annoying.
Annoying supports to play against.
-Nunu
-Taric
-Lulu
NOTE *DON'T LET YOU OPPONENT BE IN ADVANTAGE WITH MINON FARM*!!
Best supports for Ezreal would be Taric and Kayle.(This is my opinion)!
Why Taric?
-He can stun your target and you can get in advantage with your skills or you can run away when he stuns the enemy.(Ofc he can heal you)
Why Kayle?
-Because she's really really aggressive(a lot of range and slow skills) and handy she can heal you a lot and save you anytime with her ulti.

Runes are mostly up to you but this are the runes i use and most of players do,i don't want to give a big speech about the runes.
Why would you start like this?
-So you can farm easier and make a lot of damage,that mean's don't push your lane until you get your boots.
Don't forget to sell the doran's blade for last whisper.

Items
Manamune- First item way cheaper than BT, it will give you tons of mana and also epic for pokes.
Trinity Force- This item is just epic for Ezreal, buy it once and you'll understand why.
Berserkers boots- Attack speed way better than Cool down boots etc.
Blood thirster- Life steal, tons of damage.
Guardian Angel- Defense, survivability.
Last Whisper- Armor penetration/Damage.
Masteries
Typical nothing new.

Runes
-More Lifesteal less damage.
*UPDATED ON THE REQUEST*

Rush for Manamune so you get it to the max when the late game comes, this will be your strongest item in game.
Never engage first and always make sure that you are protected.
When you get your Manamune at the max level take the blue buff for Q spams.