Ezreal can be played two ways as attack damage, striker, and strength. Striker meaning he uses his basic attacks, and part of his skills, to do his damage and strength meaning he just stacks straight attack damage. This build focuses on building Ezreal as a striker, focusing on a little life steal and high critical, sort of like a normal adc only a little different.

Pros
-High damage if played
-Good Range
-Able to flee from battle or stay in pursuit with others

Cons
-Challenging champion to get used too
-All skill shots making it sometimes difficult to hit enemy's
-Can be taken down easy

Ezreals passive, Rising Spell Force, is a great passive, every time he uses a skill he gains a lot of attack speed for a decent amount of time. This allows him to use all of his skills then have enough attack speed to easily finish the enemy with basic attacks
Ezreals first skill, Mystic Shot, is a strong skill shot that applies on hit affects like a basic attack, this mean it will allow life steal, critical hits, and my favorite, the Static Shiv. This is a hard to hit skill shot that does a lot of damage, get it first and max it first.
Essence Flux is a strong nuke that does more damage on AP Ezreal but is still good on an AD one. This is also a skill shot but can go though minions making it easier to hit then Mystic Shot but also has less range. Get this third and max it second.
Arcane Shift is a highly mobile skill and Ezreals only escape, save this skill till near the middle of the fight when your sure you can finish them off, or if you think they might run, save it for when they try to get away. If you are cornered Arcane Shift can be the only thing separating you from safety, it can teleport you over most walls like flash only it can be used a lot more often. Get this second and max it last.
Ezreals ultimate, Trueshot Barrage, is Ezreals strongest skill, it does damage to everyone it encounters dealing less damage for each enemy it hits at a minimum, the range on Trueshot Barrage is endless, it is a global so it will reach from across the map allowing you to snipe those nasty teemos that escaped your Arcane shift.

I got a couple of complaints about how my build didn't have enough defense in it, too much attack damage, so I went ahead and fixed that. I replaced some of my attack speed items with more reliable items. first I replaced the Phantom Dancer with a Last Whisper and moved it to more early game, this is so that when facing a tank (or even when your not) you can still take them down without having the stress of your attacks hardly phasing them. Second I took out the Infinity Edge and replaced it with a choice of any of the defensive items I put in the build, this is so that you can have more sustain in battle.

For masteries I did something vary unusual... I had all my points spent in one tree, this is because I feel that Ezreal would benefit a lot more with the extra damage. I also put the points in what I find necessary, I focused on enhancing his basic attacks with masteries like Spellsword and Frenzy. For runes I focused on getting more out of your basic attacks and getting your basic attacks to go faster, for Seals I went Seal of Attack Speed so that you could more frequently attack getting the most of your damage, for marks I went Mark of Hybrid Penetration this is because this build does have a little bit of magic damage so you can still get the most out of those skills too, for Glyph and Quint's I went Glyph of Attack Damage and Quint of Attack Damage for obvious reasons, so you could do more damage in general.

Thanks everyone for giving time to read this and look at my build, I know this build may seem odd in some ways but give it a try, you might like it. If any of you have any suggestions on how to play ezreal, I am always willing to try new things, thanks again C: