Welcome to my Ezreal guide. I may not be the best player in the world, but this build has worked quite well on Bot as the AD Carry.

Pros;
Very high poke
Passive attack speed buff
W Gives your team attack speed
Long range
11 second CD flash
Global ult

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Cons;
Difficult to land main damage abilities such as Q
Very squishy
Very low damage if under fed
Completely useless except for attack speed buff if under fed
No stun/CC

R > Q > E > W
That's the only way to go unless you're AP

Take Boots and 3x HP Pots if your support has no sustain, or a Doran's Blade if you have Taric, Soraka, Karma, or Sona.
Farm as much as you can until you can get a second Doran's blade and grab Berserker's Greaves. You could also instead of getting double Doran's, get double Long Sword to get your Brutalizer faster. Continue farming until you get your Blood Thirster and fill that up as fast as possible. By the time that's done you should have enough for your Black Cleaver. Once you get this, you'll start doing a ton of damage. Final items should be Infinity Edge and Phantom Dancer, and I sell my Brutalizer for a Warmog's for extra survivability.

You're going to want to ask for blue often at mid game as you go OOM very quickly and will not be able to do good in a team fight.