Pros:

Nice range damage.
Fast combo of damage.
Hard to cacht.
No mana problems at mid game and at late game.
Nice ulti to dont let enemy escape or to help team when you are far away.
Have a flash "E".
You can be mid, bot, top or even solo top!
OMG, HE DANCES HARE HARE YUKAI, LOL.

Cons:

Low HP that makes you 1 or 2 hit most of times.
Bad against tanks.
No Stuns, No fear, no silence...
Bad against Stuns, fears, silence...
Not easy to play.
Maybe mana problems at early game.

Ok, first of all, The tear of the goddes, is in order to stay more time on line and most important of all, to be able of spamming spells without running out of mana. Then i pick the Jonian Boots in order to gain some cooldown reduction. Then i pick a hextech so i can have some more spell damage due to AP and have some Spell vamp so i can heal my self. Now i decide what i need most, or more cooldown reduction or maybe i need more spell vamp. If i need more spell vamp, i take the will of the ancients but if i need Cooldwon i take Nashor tooth begining with a fiendish codex, with the nashor tooth i get a nice cooldown reduction some nice AP and some useful attack speed. Now with all this bought i must decided if buying an archangel staff or the manamune(look what tanks are wearing and what your teams need for example) Now to end all, a rylai can be useful making your ulti stronger and letting you more HP so you can endure more in fights or you can pick a Tryniti force. A Lich Bane is pretty good too with this build.

I used this build for a long time and dont have much problem.

As marks, the better option i found was magic penetration in order to make more damage with "W" "E" and with ulti.
As Glyphs, I took Ap per lvl because at begining im practically ok, so its to make easier late game.
As seals, i take or Ap per lvl or cooldown reduction if i think i wont be able to take cooldwon reduction at begining.
As Quintaessence, i take the +5 Ap in order to have a nice ammount at beginning.

Yep, all masteries are in order to have more AP, Cooldown redution, Some attack speed, but most important is "The executioner" Which will make you a nice killer when enemies are running away from you.

Well, 1º skill must be Mystic Shot (nice damage, not much cd, useful in all senses), then at lvl 2 take Arcane Shift (Help you making lots of damage and run away) and at lvl 3 take Essence Flux. Now you max Arcane Shift all you can. And its like this 1º Ulti (If you can, ofc) 2º Arcane Shift and 3º It depends, if the enemy team is full of AD's with a lot of attack speed and you have some in your team too, Then max Essence Flux if not max Mystic Shot.

I hope its pretty clear.

Yep, Even with Arcane Shift, i take a Flash which can make you escape easily against the enemy team if you combo with Arcane Shift. This is a must or you can take ghost too.

As second, i usually take Ignite, but in dominion Surge is a nice one too. You can take Clarity which will make your early game more easy but this will be a bit waste at late game. Exhaust is not a bad option too ofc.

To sum up, Your role play must be like a spell spammer wich will make the enemy's life going down, slowing his attacks ,dont letting them escape and ofc help team with long range spells.

This is my first guide, even thought my main is Vladimir, lately i have been playing Ezreal "The Hare Hare Yukai Dancer" and i found joyable to play Ezreal like this (Yeah, with dancing too).

Comments will be apreciated and pls, if you have a bad comment, at least try to be polite. Thanks for reading.