First of all i want to say i don't speak english that well and if you notice some grammar issues plase let me know. About the build: This is my basic ezreal build, high damage Mystic Shot and high Autoattack damage. Because he has 2 escape abilities i think a glasscannon build works best for him.
I hope you like it!

Pros

• Good in every stage of the game
• Big burst with Mystic Shot
• Thanks to the 25% crit chance and the big, around 400
  AD your auto attacks deal a lot of damage
• You can farm from a safe distance with your Mystic Shot
• Has a global Killsecure Ultimate
• Has a low cooldown flash Arcane Shift

Cons

• Skillshot based champion
• Can be Manahungry, if you spam your Mystic Shot
• Early laning phase can be really hard

Some tips:

• Don't waste your Mystic Shots on minions, only when your enemies zones you, if you have mana issues maybe this is your problem
• Your abilities hit invisible targets as well.
  You can use them to check bushes too, if you use Essence Flux you can tell how many enemies are in he brush just by watching your passive stacks
• Using your Ultimate at the begining of a fight, gives you all 5 stacks of your passive if you shoot it correctly, and damage the whole enemy team.
• Save your Arcane Shift for positioning yourself or running away, rather than jumping in a fight. You can us it first if you have Flash or if you feel like you are safe, but without Flash and wards it's your only escapetool
• Cleanse is a really good secondary summoner spell, pick it if you face hard cc, or something like zed's Ultimate .