Ezreal is in my opinion one of the best ranged carries in the game, he has the ability to harrass alot early game because of his mystic shot which has a short cool down and a long range, not only this it can also be shot though walls which is great if people are escaping into the jungle on low health.

Pros
Great harras
Distance closer
Great escaping abilities (teleport over walls)
Deals ALOT of late game damage


Cons
Squishy, especially early game
Vulnerable to CC
Difficult to get kills early game

Ghost I like to take Ghost because it gives the ability to chase for the kill if arcane shift isnt enough, but not only does it give you the ability to chase, you can also use it + arcane shift to escape ganks etc.

Exhaust Exhaust goes well with any AD champ, mainly because they cant get outside your range and it also reduces the damage they do if you are put into a 1 v 1 situation that is quite even. It can also be used to aid in escaping if the enimie has a way to follow you over walls.

Other possibilities
Teleport Teleport: is useful to get back into lane quickly or jump across the map for a quick gank.
Flash Flash: is good to escape major ganks, but you have arcane shift which is pretty much a flash.
Ignite Ignite: can be useful for that 'little bit more' damage if they are getting away on very little health, but again the auto attack after arcane shift usually works for this.

Masteries focus mainly on offence, this is because your primary role is to be a ranged carry, meaning you need to be able to dish out as much damage as possible. You need to be getting as many kills as possible to help out your team. Points relating to ghost and exhaust, if you arent using these you can put them on anything else.

This move is great if you can keep it stacked, it gives you early game attack speed. If you can keep hitting mystic shot and essence flux your attack speed is increased a bit which is quite a handy passive, this allows you to make more hits in quicker concession keeping your passive attack speed up, which as I said is quite handy.

This is one of Ezreals core moves, it is great for harrassing enemy champs and late game it does a substantial amount of damage. It has long range and travels quickly, it is also great to last hit champs that are fleeing into the jungle because being a skill shot it goes though walls.

This is the least focused move, it scales off AP so isnt very strong in the AD Ezreal build, but I reccomend putting a single level in it at level 4, pure because it can be used for early game harrasssment, arcane shift to them and use both mystic shot and essence flux to maximise early game damage.

This move is pretty much a free flash with bonuses. It is a blink that attacks the nearest enemy for increased damage. It is great for cllosing gaps between you and enemy champs but also it can be used to escape ganks etc.

This is Ezreals ultimate. It is one of my personal favourite ults in the game, it crosses the entire map dealing damage to any enemy (champ or minion). It is great for getting last hits on champs who have fled on low health, it can also be used defensively such as if your nexus/inhib is getting annialated by creeps you can use your ult to easily wipe out a large amount of them saving the structure and getting you alot of gold.

Greater Mark of Desolation Armour pen, what can I say, damage damage damage. armour pen translates directly into damage and damage as Ezreal is good. Your main job is to deal as much damage as you possibly can and armour pen helps to acheve that.

Reduced cool downs, this is great because it allows you to harrass with mystic shot more reguly and it decreases the longer cools downs on arcane **** and trueshot barrage.

Increased attack speed, this is really helpful early game as it increases your base attack speed.

Greater Quintessence of Desolation More armour pen, this as I said translates directly to damage and the more damage the better, and these guys add 3.33 armour pen each! That adds a nice little bit of extra damage.

This item is great, the buff is in my opinion the best for any AD hampion, when an ability is used it makes your next attack do an extra 80% of base damage. I suggest to get this first because it gives mana which is helpful, and it give you a damage advantage over most of the other champions.

I reccomend taking these boots because obviously it gives speed which is always good, but also gives attack speed, this along with your seals gives you a nice little attack speed advantage.

This item is one of my personal favourite items in the game. It increases just about every stat by a decent amount AND has the sheen buff. It's just a great item in general.

This item increases your attack speed, movement speed, and crit chance all by a substantial amount, this is a great item one which I include in pretty much every AD champion build.

This stage in the game, you are fast. Your movement speed and attack speed are plenty fast now its time to start racking up the damage, and a bloodthirster is a good place to start. I reccomend it now because its still early enough to get the stacks and with your attack speed the life steal is great for survivability.

This item just straight up increases the pain you cause. The armour reduction further increases the damage you are dishing out, you add that to the B.F swords damage increase with some added attack speed, it's great.

This is the stage in the game where you are killing people left right and centre, and this item is just to top it off, it's making your auto attacks crit for anywhere between 800 and 1500 and you can kill the enemy champions in literally seconds.

Just to finish off, Me and a friend both find this build amazing for pretty much all AD carries. Your late game damage is just phenominal, you can go up to anyone but the tanks and kill them in seconds, even the tanks themselves dont take very much longer.

Thanks for reading and make suggestions to better this guide in the comments.