Hiya!
This is the guide that (with some practice) will give you a high amount of kills and assists and will lead your team to many glorious victories.
Ezreal is a fantastic champion that always will be a great choice for your team. With this simple (but detailed) guide I will try to help you summoners to get the most out of him, just the way I'm been doing for a while.
This guide is both for beginners but also can give you veteran Ezreal players some good tips.

I'm sorry for every grammar mistake and such, english is not my native language, I'm a proud Swedish wiking.

Pros:
Great mobility thanks to his E
Very hard to kill with double flash
Great amount of damage
Based on Haruhi Suzumiya
Best dance in game
Awesome ulti


Cons:
Only skillshots, so takes practice
Squishy
Gets focused alot
Being mistaken for a girl

Clarity and Flash are my usual picks.


Clarity for the extra mana ofcourse. Early game Ezreal require a lot of mana, due to both harassing, but also last hitting. It's a good choice for him all the way through the game. It can save your life a couple of times when your out of mana and need that flash and your summoner spell is on cooldown. It's also very good to have if a small teamfight starts in the river and your out of mana.


Flash is for both trollin' and survival. But also for tower diving when your at low hp. Many would think that flash is unnecessary when you have an in-built flash, but think of it two ways. 1. No one will catch you with double flash, even if the get a slow or stun at you. 2. Tower diving. Your low at hp, you can only take hit from the enemy's turret, your out of reach for a mystic shot. Take your Arcane Shift in, shot a Mystic Shoot, flash out. BOOM a kill and you survived.


If you feel that mana is not a problem, you can also choose Ignite to secure that no one gets away with low hp.


Ezreal has no Crowd Control, he usually doesn't need it because of his high mobility, but if you feel the need for a great CC tool you can pick Exhaust to really slow a hero down, the bad thing on this CC is ofcourse it's cooldown. Same as Ignite.

Greater Mark of Desolation Greater Quintessence of Desolation
With runes I take a pretty huge amount of Armor Penetration to deal some extra damage the whole game through, but it's pretty awesome early game.


Because Ezreal is really squishy I also give him some extra armor, a really wise decision.


And to be able to spam that mystic shot even more, and also to get your in-built flash back even faster I get some cooldown reduction glyphs.

As for masteries I get 21-0-9 to get the most damage possible, and 9p in utility for the extra duration with buffs. Ezreal becomes really really strong with the blue buff, so try to pick that up as often as you can.

Doran's Blade is a perfect start-item for Ezreal because it's gives him that little amount of extra damage to easily harass and do a good amount of damage but at the same time it's even more easy to last hit minions. But if your going mid or without a support you can also go with boots and hp-pots for a longer phase before you have to recall.


At the first recall I always buy Boots and Sheen. Sheen is awesome together with Ezreal's Mystic Shot and it will give you the extra amount of mana that you'll need. If you can afford, also buy Inoian Boots of Lucidity to get that cooldown to be able to spam your mystic shot when you get into a fight, or having trouble last hitting with your auto-attack.


After that I rush Infinity Edge, when you'll get that you will be doing tons of damage. Always buy the B.F. Sword first. Many people say that Infinity Edge is a bad choice on Ezreal. But I believe that they are wrong, first of you'll get sooo much damage, secondly your auto-attack get bursted really well if you get that crit, and it works well both with Sheen at first, and then later with Trinity Force.


If you can afford, buy a Vampiric Scepter, it gives you a nice little extra lifesteal.


Now it's time for your Trinity Force which is a great item on Ezreal. It applies on about everything that Ezreal is and does. It gives attack damage for your mystic shot and aouto-attack. It gives you ability power for your Essence Flux, Arcane Shift and Trueshot Barrage. It also gives you some extra critical percent, that means that it makes your Infinty Edge even better. And it has 35% to slow an enemy, and also you will deal extra damage efter you use a spell. I can't say this enough, THIS IS A MUST on Ezreal.


Now it's time for Bilgewater Cutlass and Last Whisper to get your attack damage up even more, and to get more lifesteal and armor penetration.


A Hextech Gunblade to finish your Bilgewater Cutlass with some ability power, to deal even more damage with your W, E and ofcourse ulti. The spellvamp is very handy and get you some hp back everytime you deal damage to someone. (Don't forget to use it's active, it deals 300 damage and slows the target for 3 seconds.)


And at last you will buy a Guardian Angel for two reasons. 1. You will sustain more damage. 2. The most important reason. As Ezreal you will be the one who deals the most damage in your team, so the enemy team will focus you first (if the have any kind of intelligence). And if they will succeed and kill you, your team mates will both be dealing a lot of damage at the time the enemy champions kill you, and when you will respawn your teammates can protect you so you can start deal all your damage again! It's a lifesaver.

I always max my Mystic Shot first. That will be your main damage through all game. Because when you have your cooldown later, you will be able to use this ability every 1.5-2 seconds, that is amazing. And early game it's also useful to last hit minions that are out of range for your auto-attack or you have to get them down quickly. Use this, a lot!


Your Essence Flux is a good ability to have, but not to use early game. If you find yourself in a pinch it's a good spell to use for some extra damage. But seriously, it drains to much mana from Ezreal who already lacks of mana early in the game. So never ever use this, unless you really have to, to get that kill or scare away an enemy who thinks he has a chance to kill you.
Mid game and late game this is fantastic skill to have, both cus of the damage it deals, which will be a lot with Hextech Gunblade in your hand. But also to reduce their attack speed for five seconds. Try to hit as many as possible, both in your team and in their team when you use this, because it does not only reduce their attack speed, it also boosts your teammates. So because this is mostly a late game ability I max this last.


Arcane Shift is your very own in-built flash. But it's much better than flash in many ways. First of, it has much less cooldown. Second, it does not only flash, but it also gives you an extra attack of magic damage that late game hurts, a lot! The only thing flash is better, is that it has a little longer range, and also it's faster, so if your standing in Lux ulti or something that is life threatning, use your Flash. I max this second.


Your ultimate Trueshot Barrage is one of the greatest ultimates in the entire game. Ofcourse I max this as quickly as I can. It's great to use when their is a team-fight and all enemy champs is packed together, it's great to finish of a champion who thinks he/she can outrun you at low hp, it's great for towerhugging champs at low hp in another lane. So tell your teammates as soon as you ding level 6 so they can tell you if someone is towerhugging or teleporting back with low hp at their lanes. Because of it's kinda low cooldown, don't be afraid to use it, and you now the best thing, it's cooldown lowers every time you use a skill. It's great to farm with your Mystic Shot sometimes huh. One important thing, don't try to shot it through minions, because after every unit it hits it will deal 8% less damage.

Early and mid-game almost all you do is farming. Because your items are very expensive, so you need to farm farm FARM. (And also pick up their blue whenever possible.)

The best way to do this, is to go with a support at bottom lane.

My favourite lane-partner is Sona, who will heal you every fifth second, but also does a fair amount of damage to your enemy champions in your lane. Her role is only to let you get every minion, and I mean every minion, to heal you, to help you when you have the chance to harass or possibly pick up a kill and to ward.

Soraka is also a good choice, and if your going with Soraka, pick Ignite/Exhaust instead of Clarity. But she does less damage, and her cooldown on her heal is to long for it to be the best choice.

The real game for Ezreal starts when he first picks up Infinity Edge, but the party begins when the Trinity Force arrives in your pocket.

I hoped you enjoyed reading my thoughts, and I hope that they will be a big help or at least some help to you summoners out there looking for an Ezreal guide to dominate games with.

If you have any thougts or suggestions, just comment below and we will talk about it. If you have any criticism, just add that too, but be gentle, this is my first guide ;)

God luck and God bless!

/BoGiertz