Hey guys, welcome to my "Ezreal, The Hybrid Carry" guide.
This is the build I use on Ezreal, in order to play him as an attack damage carry, but also take some advantage of his skills giving him some ability power.
As a carry, Ezreal need to farm a lot, though the cost of the whole build is actually very cheap (11930 Gold + elixirs), the intention of this build is that you can get it really fast.
You also need to play really defensive on team fights, and try to deal damage from a distance, because Ezreal is a champion really easy to kill, and you shall take advantage of his ranged skills in order to be useful for your team, by dealing damage and stay alive.

This is also the first build/guide I do here on Mobafire, so it's probably not very good, but I will be working on it in order to improve the quality of this guide, and I hope for some tips of you guys in the comments below.

I couldn't found the armor pen/magic pen marks and quintesences, that are called Greater Mark of Destruction and Greater Quintessence of Destruction, on tier 3, so I used armor penetration on this guide, but i totally recomend you to use armor pen/magic pen, because the damage you can deal physical damage and magic damage.
For the other two, I choose Greater Seal of Replenishment and Greater Glyph of Scaling Cooldown Reduction.

This allows me to cast my spells often at early game. That's very important that you can be able to cast spells to harrass you enemy or enemies, or even farm, without going out of mana.

For Masteries, I take 0-9-21, doing some health and magic resist on defense and taking mana regeneration and cooldown reduction on utility.

I always start with Doran's Ring, because of the early health and mana regeneration, and next i buy Doran's Blade, for attack damage and more health.
Because cooldown reduction is very important on Ezreal, alowing him to cast his spells more often, my option for the boots is Ionian Boots of Lucidity.
Now it's time to start dealing some damage! And for that, my options are Trinity Force, Hextech Gunblade and Guinsoo's Rageblade. Those three items are amazing for Ezreal not only because they have attack damage and ability power, but also because of their actives and passives:
Trinity Force - The passive: after using an ability, your next basic attack deals bonus physical damage equal to 150% of your base Attack Damage, also applies on Ezreal's Mystic Shot;
Hextech Gunblade - You can activate this item to deal 300 magic damage and slows the target champion's Movement Speed by 50% for 3 seconds;
Guinsoo's Rageblade - On basic attack or ability use, increases your Attack Speed by 4% and Ability Power by 6 for 5 seconds stacking up to 8 times. This items's passive and Ezreal's passive together can increase his attack speed up to 82%.

Other usefull items for Ezreal:

Manamune
Archangel's Staff
Nashor's Tooth
Deathfire Grasp
Mejai's Soulstealer
Sword of the Occult

For Summoner Spells, I like to use Heal and Flash, but I think that most of the Summoner Spells are good for Ezreal, like Clarity, Exhaust, Ignite, Surge, Cleanse, Ghost and Teleport.
You must choose the Summoner Spells that fit with your play style, and attempt your needs through the entire game.

Heal - I use heal because sometimes I'm the focus of the enemy team, because i'm too weak defensively, but it can also be used to trap your enemies, making them attack you while you're low on health, and then use heal and finish them off.
Flash - Can be an useless spell for Ezreal, because his Arcane Shift already teleports him to a location nearby, but sometimes you can be saved by those two spells.
Clarity - Can be really helpful at early game, but useless late game.
Exhaust - The favourite of the carries, it can save you in a 1vs1 and even give you a win.
Ignite - If you feel like you don't deal enough damage, then this is the Summoner Spell.
Surge - Also a great Summoner Spell for Ezreal, can be decisive in a 1vs1 or in a team fight.
Cleanse - Works out like Heal. If you're the focus, this is the Summoner Spell.
Ghost - It's a Summoner Spell that can be used offensively, to chase an enemy, or defensively, to escape from an enemy.
Teleport - Can help you staying in lane more time or ganking other lanes with wards.

Well, that's it, I hope I can help you with this guide.
Please comment, and feel free to complain and give some advices.