THIS GUIDE IS COMPLETE but incomplete at the same time as of now (4/22/2012) I have changed my recommended summoner spells, masteries, items, and runes therefore when I have time I need to change the description in those categories. -There is no information or explanation on AP Ezreal(Team 2) I apologize if it is any inconvenience.

I kindly ask you to read what is present in the build and then try it out in a few games before commenting or voting. Thank you.

Pros:
-Faster than a cheetah
-Any range ult Trueshot Barrage
- Arcane Shift - Great escape ability
- Essence Flux - Gives AD teammates more burst and reduces enemy AD attack speed
-Phenomenal mid lane champ (bot lane with support also works great)
-'Spammable' Skills
-Ult rarely on cooldown
- Trueshot Barrage Nuke

Cons:
-Squishy
-Focused in team fights
-No CC

Yes, I realize that there are SEVEN item in my purchase Sequence. I suggest you decide between IE or GA, I don't suggest getting both. OR another route one could take is wait until the end of your build and sell your IE and buy the GA.

Early Damage???: NOW, something that can be done to change early game damage is buy B. F. Sword before the Phage and Bloodthirster after the Trinity Force. I have noticed that if you get fed with this build and follow it item for item then you don't do as much damage as normal carries would. SO, that is how you fix that problem!

Infinity Edge - This item can be swapped out with whatever item you or your team may be needing. Maybe a champion you are facing is focusing you non stop, you can buy a defensive item to counter their damage. Items that can be switched out for it offensively are: Black Cleaver if the enemy is heavy on armor AND Madred's Bloodrazor if the enemy is high on health. There are other offensive items that can replace Infinity Edge I just prefer these.

Youmuu's Ghostblade - Yes this items activation increases attack speed for melee champions. However, this item is great for early/mid game and occasionally late game. It provides a whirl of stats: Arm Pen, Crit, Damage, Movement Speed/Attack Speed (activate), and CDR (Cooldown Reduction). If the game is lasting extremely long and its a close game and you have your full build you may sell Youmuu's Ghostblade and buy whatever best counters your enemy.

Ezreal's ult Trueshot Barrage is the only ult besides Ashe's Enchanted Crystal Arrow that can go ANYWHERE on the map. It can be used for quite a few things; Sniping/initiating/harassing/clearing minion waves/backing off opponents from your turret/and the least useful: waiting at the end of a team fight to kill one person but your team is already in trouble. Ezreal should always use his ult at the beginning of the fight (as soon as it starts), if he is not doing that then do it before the fight to initiate or when possible!

Ezreal's ult Trueshot Barrage can be used almost everytime that it is available. To do this all you have to do is constantly hit enemies and minions with your Q Mystic Shot, if you do this, YOU'RE GOLDEN! Just like his big wavy hair!

Sometimes you will encounter an enemy face to face where you are almost standing on top of each other... A fun thing to do if you are in this situation is Trueshot Barrage then Arcane Shift on top of yourself then Essence Flux and finally Mystic Shot for the kill if they aren't dead yet! Usually they die after the first Mystic Shot. Most people are taken off guard.

Essence Flux - Okay I don't know why the majority of people that play Ezreal wait to get this spell at the very end of the game. It is extremely useful for your team. You speed up everyone's attack speed which means more damage which means better team fights/ganks. It also reduces the enemy attack speed by the same amount that it buffs which is good for temporarily shutting down an AD enemy. A great use that I get out of it is when killing dragon I Essence Flux my teammates and we kill very quickly and makes it safer for us because we are less likely to be ganked if we 'get in and get out'. Many times I Essence Flux a teammate or two when pushing a tower and we down it quickly before an enemy can reach the turret. This is why ALL Ezreal's should get Essence Flux in early/mid game!

Arcane Shift is your best friend when playing Ezreal. No matter what build you use this will always be your number one escape, it will always be there! You can jump over walls/juke by changing direction/dodging a skill shot/chase an enemy/poking and more.

Greater Glyph of Scaling Mana Regeneration - Helps with lane sustainability
Greater Glyph of Scaling Attack Damage - These Glyphs can be switched out with any Glyphs you prefer. I enjoy the boost of AD Damage for the entire game (especially mid-game).
Greater Seal of Scaling Attack Damage - These Seals are my best friend... they add 10 AD overall and that is a nice amount- you're are auto attacking a fleeing champion and its 10 more damage than you would of had. It does a lot of damage over time..
Greater Mark of Desolation - Almost all AD Carries get 9 Arm Pen Marks, Armor Penetration is very crucial and useful for early game.
Greater Quintessence of Movement Speed - An extra boos of movement speed, doesn't hurt? It can easily be switched for Greater Quintessence of Desolation.
Greater Quintessence of Scaling Attack Damage - At level 2 you already have 1 extra point of AD! At level 6 you have 3 extra AD! And at 18 you have 9 extra points of AD, it's better for early/mid-game but EVERY STAT COUNTS!

Utility Changes:

To start, you may put 1 point in Utility Mastery instead of Greed . I usually point my last point in Utility Mastery but have recently been using Greed for that extra gold boost!

Offense Changes:

Another change would be taking 2 points out of Brute Force and putting them in Lethality . It all depends on what the summoner prefers!
I enjoy Brute Force for the early/mid game edge-Every stat counts!!!

Another optional change could do is take a point out of Archaic Knowledge (WHICH I DO NOT RECOMMEND) and one point out of Sorcery and put the 2 points in Lethality .
The reason that I do not recommend this change is because Ezreal's Ult Trueshot Barrage deals Magic Damage.

Exhaust - Exhaust can be used as a last resort get away if you are in trouble. Use it to slow your enemy down and escape or to save your teammate from getting killed. Exhaust is also great for shutting down the opponent carry or support (heavy healers). The spell can be used to get your team that kill that changes the game when you are all chasing the enemy carry that is alone! Your team then pushes on to victory!

Ghost - Ghost... it is what puts you at cheetah speed levels. You can move from your Nexus to middle in approximately 6 seconds with full build and Youmuu's Ghostblade active.

OPTIONAL SUMMONER SPELLS:

Flash - A different version of escaping. I do not get Flash with AD Ezreal because I have enough speed plus Arcane Shift to get away from most trouble. Although it is fun to Arcane Shift over one wall and then Flash over another to get closer or father away from an enemy champion. Another use with Flash could be in a situation where you know someone is fairly low at their turret and they are trying to B. What you do is Arcane Shift over the wall so it hits them, do your combo then Flash back over the wall. I only advise to do this when you have a fair amount of health.
Ignite -If no one on your team has Ignite and you are playing draft mode and see you're facing champions like Sona, Soraka, or Dr. Mundo then grab Ignite.
Cleanse -If you want to be the ultimate master of escape then grab Cleanse + Ghost. Use Cleanse when you get "cc'd" and Arcane Shift away. It can also be used for chasing if you get slowed or stunned.

Okay-farming is very easy with Ezreal if you are the type of person who wants to sit in lane for an extremely long time. 90% of the time the only problem Ezreal has with farming is that he'll get harassed too much in early game.

AN EXAMPLE is that you are bot lane with a champion like Janna and she cannot heal you like Soraka, Kayle, or champions of that nature can. So a way to fix your farming is grab Sapphire Crystal and Meki Pendant the first time you B so that this way you can Mystic Shot constantly and grab CS (Creep Score).

In other situations when you are in lane with support like Taric or Soraka you CAN play aggressive and save your mana and LAST HIT minions with auto attacks. Then you use your mana for harassing champions in your lane with everything you have. This way generally you can control your lane. A great combo is Tarics Dazzle and then your Exhaust + Arcane Shift + Mystic Shot and finish with auto attacks as best you can with additional Mystic Shots

CANNOT WAIT FOR THE PULSEFIRE EZREAL SKIN O_O.
Stay friendly!

This guide has been updated on January 08, 2012 - disregard the comments.
Last update of guide April 22, 2012 - Still needs fixing on descriptions like stated at beginning of guide.

Thanks

-Stealth Ops