Ezreal was my favorite champion for the longest time. It was sad to see him fall out of the scene due to stronger AD carries but now with new changes, Ezreal can be played at a higher level with this build.
This build provides utility, damage, and the ability to kite. Your chances of being caught are really low with a 3-4 second CD on arcane shift only if you hit a couple mystic shots.

I like taking these set of runes because armor pen really helps your damage. Armor pen is a lot better than physical damage runes late game. You guys are probably wondering why aren't people using it. To explain this, you will need to understand that physical damage on champions like Graves, Caitlyn, and Varus require AD runes to be relevant early game. This is because they have skills like buckshot and piltover peacemaker. They are able to push the lane and pressure. However, its harder to push the lane with armor pen runes.

Reds Armor pen, I feel Ezreal is really weak without Armor pen
Yellows Armor, best in slot for trading and sustaining
Blues MR scaling, I take MR scaling because its a lot better late game and I just opt for late game as an ad carry
Quints I take life steal quints because I start with [items/dorans-blade.png] and it adds onto the sustain in lane.

I take these 22/4/4 because I want the effects of butcher, havoc, and sorcery. These effects are really good for Ezreal. You will need to take 4 defense in for the extra durability and of course mana regen from the utility tree.
You will need butcher to last hit on Ezreal. You will find it really hard to last hit with armor pen runes, that is why I take the butcher mastery.

This is what I usually take because it helps your laning phase a lot. You can use it at the start of the lane to gain the 5 damage+AP from masteries if you want to bully your lane more.
Explanation:
I also take these masteries sometimes for survivability against high burst enemies.
If you aren't going to take ignite take barrier, no reason for [summoners/cleanse.png]
really hard to catch Ezreal already.

Passive: Rising Spell Force

Explanation:

This passive is great, it's like a free 50% attack speed at the start of the fight if you open with [skills/ezreal/r.png]in lane. If you can stack up to 5, you will not lose trades because you will have 50% more attack speed than the opposing enemy.

Q: Mystic Shot

Explanation:

This is what makes Ezreal a great champion. This has a very low cooldown if you can hit an enemy. It has a 1 second cooldown if you have 40% cdr which is really to get for ezreal, he has 38% with the full build.

W: Essence Flux

Explanation:

I generally use this to just keep my [skills/ezreal/p.png] stacks up. It's decent for taking out turrets and doing Dragon/Baron. Of course, you use it on your allies for the stacks ^^.

E: Arcane Shift

Explanation:

Arguably the best spell for an AD carry, it's literally a free flash if you hit [skills/ezreal/q.png] 2-3 times. Once you use [skills/ezreal/e.png] the CD is about 3 seconds, you can use this spell offensively in lane if you have good ward coverage on the map. You have to be smart about using it though and only go in when you can win this. This will come naturally through lots of experience and practice

R: Trueshot Barrage

Explanation:

Trueshot barrage helps you push your lane. You generally want to push your lane when you want to back so you don't lose too much CS. It's also a global spell and it may help you pick up kills across the map so be sure to keep your eye on the minimap when you see lots of icons clumping together. In teamfights, you want to open with this spell for the [skills/ezreal/p.png] stacks.

level up [skills/ezreal/r.png] whenever you have it of course.
Max [skills/ezreal/q.png] first to lower the cooldowns and increase the damage
Max [skills/ezreal/e.png] after [skills/ezreal/q.png] to lower the cooldown on your primary escape spell
and of course [skills/ezreal/w.png] last its generally used to only keep up your(passive) not really a damage spell.

I build Ezreal with the new blue build
starting with [items/dorans-blade.png] for the laning phase and then going [items/spirit-of-the-elder-lizard.png]. This item is actually very cost efficient, it gives you 45 damage, which costs 1550g 10% FREE cooldown reduction and mana regen all for 2000g and with a true damage passive to top it off, it gives players a huge spike in damage.
From here you can either go [items/tear-of-the-goddess.png] to start stacking early for the [items/manamune.png] or [items/frozen-fist.png] for the extra damage late game

Core: [items/frozen-fist.png] [items/muramana.png][items/ionian-boots-of-lucidity.png]

You must have these items for blue Ezreal the [items/frozen-fist.png] will allow you to hit your [skills/ezreal/q.png] with ease and [items/muramana.png] will increase your damage like mad and of course [items/ionian-boots-of-lucidity.png] for the CDR for more [skills/ezreal/q.png]

**final build was listed above**

In early game, you want to push up your lane as fast as possible. It is very bad for you to play on defense when you are using armor pen. If you do this, you will find it really hard to last hit with armor pen. It's important to note that your #1 priority is to push up to their turret and just constantly poking them down with [skills/ezreal/q.png].

The easiest ways to land [skills/ezreal/q.png] is when the enemy AD goes for last hits. Remember to be careful though, if the enemy is smart he will attack you from the back. As a result, generally Ezreal will lose the trade. With lots of practice and experience, you will evenutally learn when is the best time to trade so be patient!

Ezreal has a decent mid game with [items/spirit-of-the-elder-lizard.png] and [items/sheen.png] you will be dishing out 360 dmg per [skills/ezreal/q.png]. It is very crucial that you hit your [skills/ezreal/q.png] when a dragon fight happens most of your damage will result from that.

In late game, it's important to stay in the safest position but also always being in range to use [skills/ezreal/q.png] You can easily [skills/ezreal/e.png] out of any bad position if needed. However, if you are in a bad situation, you can just use flash but generally you do not want to be too close to the enemy unless they are in killing range.

Pros
Long range spells.
Safest AD carry.
The most mobile AD carry.
Consistent damage throughout the whole game.
Feels great to use [skills/ezreal/r.png][skills/ezreal/e.png][skills/ezreal/q.png] combo.

Cons
Fairly hard to master.
Can be caught out at level one if not in a safe position, one of the lowest base HP in the game.
Must hit skillshots, it's very crucial for blue Ezreal.
Can lose lane if pushed upon.

Have fun on the field of justice ^^