Welcome to my guide.
INTRO
Ezreal is by far my favourite character to play as it gives you a wide variety of builds and ways to use him. At the end of nearly every game I play Ezreal I have the most damage dealt. With the new patch AD ezreal has probably become a better choice but if you get into a team that is all AD it helps to be able to have a AP build ready so you can still play this Champ.

Pros
Spammable skills
Great escapes
Sniping ult
Great At last shot
Destructive burst

Cons
No crowd control
Skill shot focused
Slow movement
Squishy

Summoner Spells
Ghost Usual ranged carry, run away or chase down
Flash Back up Arcane Shift
Teleport For the quick buy and get back to your lane

{b]Skills[/b]
Rising Spell Force - YOUR DESC
Mystic Shot - This will be your way to last shot minions from a safe distance and poke any champion that doesn't hide behind their creep wave, will hit hard once you gain lich bane
Essence Flux - Your main Damage spell, try to hit as many champions as possible to gain the attack speed increase, decrease. Very useful when taking down a turret
Arcane Shift - Your main escape, chasing or dodging ability. Never use it at the start of a team fight.
Trueshot Barrage - Very useful ult that will deal a lot of damage. Can be used to snipe a low health champion. I use it when I am about to leave my lane so that my creep will push.

Masteries
For masteries I would ensure that you take the 9 in offense to gain the bonus magic pen. I also take 21 in utility to gain the most max mana and cooldowns as possible. If you feel to squishy I have seen some people take some defense, but as long as you stay away from the fight you should do well.
Runes
I chose armour pen marks and quints to make Mystic Shot must more potent at the beginning of the game

Items
CORE

Clarification:
I know that you are thinking Manamune is a AD item. Well Mystic Shot > Essence Flux early game, so I will get manamune to start so that I am building my mana but still able to deal damage. Also with the Archangel's staff it give you 40 AP as a bonus.

Situational items:
Void Staff for when your opponents are getting a lot of magic resistance
Sorcerer's Shoes boots with more damaging potential
Boots of Swiftness you are really slow, if you are having troubles flashing out of trouble get these
Mejai's Soulstealer if you feel like you are going to dominate your lane get it before getting manamune
Rylai's Crystal Scepter slow the enemy and get some hp, red lizard buff does the same thing though
Abyssal Mask if your enemies have a lot of magic damage get this to gain some MR and AP
Playstyle
Early game
This build is very dependent on having a high CS so you will want mid. Focus on last shooting minions with both you auto attack and mystic shot and poking any champion that doesn't hide behind their creep. Keep an eye on other lanes to see if you can catch a champ recalling at tower with your trueshot. If your enemy has to recall try to get your jungler or wanderer to come and help you take down the tower with your essence flux
Mid game
By now you should have enough mana to spam your skills constantly. Work with your team as you are very squishy on your own. try to hide in the side and poke through walls. When the enemy comes to deal with you flash away and hit the enemy with a true shot. Once your trueshot goes off your team should have the advantage in the fight. continue to blast away with your shots and use your arcane shift to flash back in to finish off the fight.
Late game
If you team has an initiator try to save your trueshot for halfway through the battle to kill carry at half health. poke and stay away from everyone using your flashes.

Things to consider
very rarely should you ever be near the fight. Ezreal has enough range hit from well outside of the fight. This build should never run out of mana so do not be afraid to spam your skills always.