This is the breakdown. Knowing how to play Ezreal it makes it really easy to find a good build.
Start the game with doran's blade.
Earn cash and then buy Berserker greaves then with whatever is left over buy either vampiric scepter or Amplifying tome.
Build the Sheen or Blood thirster depending on the item you picked.
Then buy the other and build up Trinity Force.
Buy last whisper to get more armor penetration.
Buy banshee's veil and then Manamune for the extra mana and hp.

Skills:
follow the build
Use Ezreals abilities to build up his passive ability for the 5 stack.
Use his ult to kill your enemy if they are running away while they have low hp and trying to tp out. (use the mini map if needed to aim)
Use Mystic shot for range and if no minions are around, use Essence flux for shorter range to hit champions (phases through minions), Arcane shot use it to escape when needed or to rush in when they are running.