After maining Ezreal for about 3 weeks now I feel like sharing my build that I have come to after a large number of changes. This is in my opinion the best build for an AD Ezreal.
This is my first build guide ever and will be edited further in the future when I get a hang of how to organize a guide.
Item Build; Early - Core - Finalized
Start off with a Doran's Blade the early game AD combined with life steal and +100 health makes it the perfect item for durability which is highly needed for Ezreal.
I usually mid and when I return to base depends on how agressive or how well my opponent plays, I usually return to base right after I grab a kill/make my opponent bluepill and which leaves me between 600-1500 coins.
On first return to base I grab Boots of Speed and a second Doran's Blade for the reasons stated above. The next Item I get for my build is the The Bloodthirster, this item is just amazing for Ezreal. High AD combined with lifesteal makes your harrasment game top tier. So if you have enough coins grab a Vampiric Scepter aswell.
At this point you should be ~Lv. 6 or so with +200 health some AD and 18% lifesteal. From here on you keep harassing your opponent and as your minions reach the turret, backtrack and go to golem ASAP. Golem buff is a must have for any Ezreal which is why I make it my job to grab both my teams buff and the other teams buff (I usually ward both/get someone else to ward it or have jungler telling me when to come to last hit golem). With the golem buff you can practicly spam Mystic Shot and with its low mana cost you will actually nearly regain mana as fast as you use Mystic Shot. After a bit of farming, which is extremely important to do well on an Ezreal as he is a very item hungry champion you should return to base and grab a B. F. Sword and eventually finnish off your The Bloodthirster.
At this point you should have reached close to midgame and should start building your Trinity Force. As Ezreal's Mystic Shot is based on AD you should be dealing nearly 2x as much damage with that as your auto attacks. The Sheen's ability to boost your normal attacks after a spell use is extremely handy when spamming Mystic Shots at an enemy champion.
So build your trinity in this order: Sheen > Phage > Trinity Force
At this point your probably wondering, but what about tier 2 boots? Well somewhat inexperienced Ezreal players might find it usefull to have the movement speed boosted up from 355 although I can easely catch up with any champion using Arcane Shift and Ghost to secure the kill if nescessary. Either way, after building your Trinity Force you have finished your core build and should actually grab the tier 2 boots. Many people take the Ionian Boots of Lucidity for the cooldown reduction, but in my opinion with CDR runes + golem buff (which, yes you should ALWAYS have) I find it unnecessary. I usually shift between two boots: The Boots of Swiftness for the enhanced movement speed lategame, this combined with Trinity Force and Arcane Shift will make you really hard to catch. However if you are facing a heavy cc team and you keep dying to stuns, snares etc. Then definately go for the Mercury's ThreadsMercury's Threads for the reduced Crowd Control effect combined with magic resistance(if your heavy CC enemys start ganking up early, you should probably get this before building trinity).
Lategame you can shift around a lot on the items. As Ezreal is squishy and highly vulnerable to CC definately get a Banshee's VeilBanshee's Veil if needed. For last 2 items I usually go for the second The BloodthirsterBloodthirster followed by a Madred's BloodrazorMadred's Bloodrazor.
If finishing your build (which is something I have only done once) your build should look something like this:
What to get:
My choice in Summoner Spells is always: Ghost and Ignite The enhanced movement speed from Ghost can be used to either chase your opponents, kite your opponents or run back to your lane if you die to secure your turret. Ignite comes in really handy for first blood and if you do get first blood you will probably be ~2 lvls ahead early game which will contribute to lane dominance. Ignite is also really handy for ezreal as he is too squishy to turret dive properly like tanking turret he can just run under it while minions are getting attacked, pop ignite on enemy champion and arcane shifting through the wall without taking damage by turret.
Other spells that might be usefull is: Exhaust I have never really liked using this spell myself, but I love it when my team members do use it, a Exhaust Ignite combo = firstblood easely.
I always run as fast as I can to mid and hide in the brush. I'd go as far to say that 35% of the time you have a enemy champion going into the brush before minions spawn and you will get first blood before minions have even spawned.
The above method must be executed well tho. At the loading screen always check your opponents summoner spells and try to remember these (or just press "O" ingame when you know who their mid is) so you dont do something stupid like diving in for a kill with low health when oppoenent has heal.
Ezreal is a really squishy champion and this makes it hard to stay alive throughout a game. What you need to remember is that Arcane Shift is a really good escape tool and should therefore be considered saving instead of using it to line up mystic shots (allthough this is a really effective method of killing someone).
The ultimate for Ezreal Trueshot Barrage is amazing, it has high damage output and works like a charm for sniping kills across the map. I have several times found myself at base while opponents are attacking turrets with low health and just easely sniped them off with Trueshot Barrage. This skill is also very usefull if you have to leave your lane or have died and minions are ganging up on your turret you can just clear the minion waves from base. Another thing about this is that when you have the golem buff and you are spamming Mystic Shot 24/7 you will regain your ultimate extremely fast, sometimes I actually get to use my ultimate twice in a team fight. This is due to Mystic Shots ability to reduce all ability cooldowns by 1 second for each successful hit.
Well I'm not really that good lategame player I'm usually at my prime during early-midgame as I am most likely targeted first for my squishyness and I have usually gotten quite a few kills and therefore I am looked upon as a big threat aswell. My best advice is just to stay in the background help your team members out as much as you can but don't dive in for kills as this is too risky.
This is basically the only time you will be using Essence Flux on an AD Ezreal. Shoot a Essence Flux on your team members to buff their attack speed (this also comes in handy in team fights, but can be difficult as your team will most likely not be in the same place to avoid aoe damage etc).
MORE TO COME.