Ezreal - The Prodigal Explorer
This is my build how I play AD Ezreal. This build revolves around Ezreal in mid.

Pros
Perfect in mid.
Spammable and strong skills.
A great escape.
Able to teleport.

Cons

Very squishy.
May take a while to master in mid.
Targeted first in team battles.
Mana is drained easily.

For runes I use mana regeneration runes, armour penetration runes and flat health runes. I chose these because Ezreal has mana problems, and need the mana regeneration. Flat health runes are great for early game and are excellent as Ezreal is quite squishy.

Greater Mark of Desolation x9
x9
x9
x3

These are the best runes that Ezreal can have.

I use 29/0/1 for Masteries. This is for a ranged dps carry. This will give you all you need to deal a lot of damage.

Ezreal isn't the best champion at farming. Just try to get the last hit on minions with your basic attack and if you have the mana regen runes, you can sometimes use your Q spell too kill minions. Use your ultimate to clear minions if there is a lot and you feel the need to ultimate them! If you need your ultimate and you dont have it this may result in a death for you or one of your team mates!

Ezreal has four spells. He has Mystic Shot, Essence Flux, Arcane Shift and Trueshot Barrage. I will explain these spells.

Mystic Shot: Single target skill shot. Your main spell. Does great damage. If you have a sheen or some life steal, that will apply to the spell as it is a physical spell. Hits anything.

Essence Flux: In an AD build this is used for the buff / debuff of attack speed great to 1v1 other dps champs slowing their attack speed or using it on your team that's pushing the tower with you. (gives passive stacks per person encountered, regardless of team)

Arcane Shift: This spell is used for escaping or chasing targets. Can teleport over certain walls. If you use this spell near a minion or champion you will shoot the target.

Mystic Shot: An across the map ultimate. Has no range just fires until it goes out of the map. This requires AP but because this is AD you wont get the maximum damage but at late levels this can take 30-60% of their life. Around 60-80 second cooldown. Good for finishing of running champions and clearing minion's pushing a allied turret.

+
I use these because when chasing or 1v1 in mid it renders the target useless. As ezreal has no cc its good to use as a slow to chase or a slow to escape. If you use this make sure you put a point into this in your talents.

Start off by grabbing a Dorans Blade and head for mid. Last hit minions and harass who ever is laning in mid. At level 6 you should get a kill. Be careful for ganks.

Last hitting

You can last hit minions by simply auto attacking or using . Last hitting is essential as it gives extra gold. By doing this you will sure be on the road to winning as a fed Ezreal.

By now you should have a few kills and have Beserkers Greaves, Sheen and have the essential items into a Infinity Edge. Start ganking and pushing towers. Don't over extend as you may get ganked from top or bottom lane. Make sure you have atleast destroyed one turret and mid is not being pushed as you wouldn't want your mid turret to be destroyed.

to clear minions on towers and last hit the runners.

By now you should have at least 6-10 kills or more and should be near to finishing the items in the build. When in team battles make sure you use to take a fair amount of damage and get full stacks on your passive ability. This will give you an extra 75% attack speed!

Make sure to ward baron at all times!

Play safe.
Last hit.
Don't over extend.
Ward baron and dragon.
Don't stay out of mana.

This build may change due to patches.