Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
Inspiration: Comprehensive Guide to AD Ezreal By: Tegea
This is purely a build. Not a guide.
I can explain why this is better than Tegea's build though.
First off, your critical hits will do 626.8444 damage, not including ArP. With ArP I would guess around 700.
Ghost: Good for chasing, or escaping!
Flash: Good for chasing, or escaping!
Why not cleanse? Well, if you don't have Willpower, don't bother.
Why Greed? In an hour long game, it'll give you 360 gold.
Why ArP Marks? Because they add onto your damage output.
Why HP Per level Seals? Because Ezreal is too squishy without extra health.
Why MR Per level Glyphs? Because without any extra MR, you'll get owned by AP nukers like Ryze or Malzahar.
Why ArP Quintessences? Because they add onto your damage output.
Doran's Shield: Uber Laning Power
Boots of Mobility: Almost as good as the Summoner Spell: Teleport!
Youmuu's Ghostblade: Damage, Critical Strike, Cooldown Reduction, Movement Speed, ArP, Attack Speed...All that good stuff!
The Brutalizer: Even more Damage, ArP, and Cooldown Reduction.
Infinity Edge: Makes your damage output from before look like Soraka's Damage output.
Cloak of Agility: 47% Critical Strike isn't enough.