Hello, my name is McMaster and I AD carry for SoCalFlame, a ranked team I'm in with some of my friends. I main Ezreal, having him be my favorite. I am very new to making character guides, so constructive critisism would help greatly. :D Now that we're past that, let's get straight into the guide!!

My LoL Cypher (first verse about Ezreal) Play Video
One of my many matches with Ezreal. Going 17-5-4.
(if you have LoL replay you can watch it from there, just click this link)
(if you dont have LoL replay, click this link and you can download the Video from there)
http://www.leaguereplays.com/replays/match/2554450/

Pros:
-Maximum damage output from masteries and runes
-Good amount of sustain
-Not as squishy as other builds early game
-Good late game Magic Resist
Cons:
-Less mobility due to taking no points in the utility masteries)
-Vulnerable to CC due to taking Ignite over Cleanse

Quints:
Attack Damage x3 - Usual quints for an AD Carry
This is because of the increase of AD can help farm earlier in the game, and pick up a first blood.

Marks:
(FOUND IN NEXT CHAPTER)

Seals:
Armor x9 - Usual seals for an AD Carry
This gives major survivability earlier in the game, especially against the other AD Carry.

Glyphs:
Magic Resist per level - Usual glyphs for an AD Carry
The reason it is MR per level is to block some of the AP Carry's burst damage, and to give you more survivability in team fights. Another reason is that that much is not required early game, knowing the enemy Carry that you are laning against usually does physical damage.

On my rune page for Ezreal, I take attack damage marks. This is mostly because it highly contributes to Ezreal's early game. My main reason for this is because of Ezreal's Q, Mystic Shot.

First, armour pen runes are usually only used on AD bruisers. Second, Mystic Shot scales 1.1 AD, leaving AD marks to result in a LOT more damage.

Triforce:

Sheen Proc. works with Mystic shot in two ways.
1. Mystic Shot has a very low base cooldown, letting you use the Sheen's passive very often.
2. Mystic Shot applies on hit effects. So if you already have the passive on you, then a Mystic Shot will activate it, doing it's base damage plus the addition scaling damage AND the Sheen proc's damage.

Phage works to give Ezreal some much needed health. Also the AD enables him to do more damage.

Zeal works on all AD Carries whether it's Twtich, or even Urgot.

These three items combine make the ULTIMATE PERFECT WOMBOCOMBO PENTAKILL SOLO BARON EPICNESS FILLED item for Ezreal!


Bloodthirster:

Ezreal can lifesteal off of his Mystic Shot!
The AD also helps his basic attacks and his Mystic Shot's ratio.


Guardian Angel:

Guardian Angel gives you just the right amount of Armor and Magic Resist to survive a team fight.

Also, in case you get focused(or jumped on by a fed bruiser) you receive a second life!
With a five minute cool down, of course...


Last Whisper:

In case the enemy builds any Armor what so ever, you can damage them through that with the massive amount of Amour Penetration you receive from the Last Whisper.


Infinity Edge:

This item gives you attack damage, critical strike chance, and more critical strike damage percentage! Perfect for an AD Carry!


Berserker's Greaves:

Last and probably least important, this item gives you significant movement speed and a good amount of attack speed.


Phantom Dancer:

There is no Phantom Dancer in this build, having it be replaced by the Trinity Force.
You mad PD??

Ezreal's Q: Mystic Shot
Max this FIRST
Low cooldown high damage spell results in maximum damage output.

Ezreal's W: Essence Flux
(FOUND IN NEXT CHAPTER)

Ezreal's E: Arcane Shift
Maxing Arcane Shift second offers a high damage combination on champions from using Mystic Shot after.

Ezreal's Ultimate: Trueshot Barrage
It's an ultimate, take it at levels 6, 11, and 16.

Ezreal's W, Essence Flux, does AOE damage. If you hit an ally with it, it would increase their attack speed(one base percentage). As an addition, it would decrease an enemy's attack speed, along with the damage delt.
After the recent patch, the attack speed DEBUFF got REMOVED from Essence Flux. Now, the only real use for Essence Flux is a small amount of base damage(that scales with ability power) and an attack speed buff for your allies(which now increases its base per ability level). This is mostly used for tower "bulldozing"(taking down enemy towers as quick as possible). Towers, unless it is the outer tower in a lane, usually don't get taken down until later in the game. This is why you max Essence Flux last, giving you the maximum ally attack speed percentage when you actually need it.