Ezreal - The Prodigal Explorer.
This is how I play AD Ezreal on mid. This build as all about going mid, so if you want to take bot with support, not sure if this build is for you, couse I personally dont like going bot.

So start off with runes. I go for
Greater Mark of DesolationNo doubt AD carry needs this, so im not gonna comment on this one.
Greater Glyph of ShieldingThis one was kinda pain in ***, couse I couldnt figure out what exactly do I want as blue runes and I couldn`t find anything better than MR.
Greater Quintessence of DesolationGreater Seal of ClarityEzreal lacks of mana all the time, so this is why you need Seal of Clarity

As for masteries I use ghost and exhaust.
- Exhaust is the best if you play mid against another AD champ, not so usefull against ap, but still. I choose exhaust, becouse it can deny opposite teams carry which is really helpfull, exhaust aslo helps for chasing and running away.- I use Ghost for running/chasing people.

What about other Summoner Spells ?

People might ask, why not flash instead of exhaust ? Well if you play smart and dont waste your E in wrong moment then there is no point of Flash. But if you want to steal baron ( or try to ) then yea, flash is realllllyyy nice, becouse you can flash in with E and flash out with FLash.
So yeah, you can use flash to, but I dont think you should use anything else.

As for masteries I go 23:6:1. Many people would say that this is kinda ******** and Ez needs more mana so they would go for 21:0:9, but I say that is ********, becouse if you know how to play you wont be spamming your spells all the time and save it for ganks and just farm with normal attack. As you probably know Ez is kinda squishy, thats why i do 6 masteries in defense 6 armor and 6 MR helps you in begginig alot, later ofc it`s not that helpfull, but still i think its better then spending those 6 talents in Utility.
So Back to case. 23:6:1
As you can see there is a point inandBecouse that extra minus 10 mr and armor is really nice if you try fb and extra speed on ghost is good for chasing and running away.
As for all other 22 points in Offense you probably know what I`m thinking ( max out dmg )

Buyand head to your lane. Play safe and get as many last hits as you can. Now there are 2 ways when to recall. If you are doing gr8, dont lack mana all the time and your opponent isnt harrasing you to much or pushing your lane, then wait till 1500gold and recall. Buy+.If your low on hp all the time and getting harrased all the time, then try to stay on lane till you get 1150 gold, then recall and buy. After you boughtHead to your lane, push it as hard as you can and useward at your dragon.You have to keep an eye on the dragon all the time and if you have boughtAfter+and the opponent jungler havent warded you can solo dragon easily.

By this time ( more to lvl 12 ) you shoulda have boughtIf you still havent soloed the dragon then this is the time you should do it. At this stage of game its really easy to solo dragon and even escape, you just have to stay at the back of dragon and get your E ready, to escape in case they come. Now that you have these items you can push your lane really easy and head for ganks or just to steal theyr blue and red, which will be really fast becouse of

Well at this stage you and your team will stick together and go for teamfights. if a teamfight starts and you see them in a nice line for yourUse it immediately, becouse this will give you max stacks of your passive. Some people useonly for last hitting opponent ( killing blow ) but thats really stupid, couse if you use it in start of a teamfight and do some nice dmg they will have a fear in them already and you have your 5 stacks and you will attack like a monster.

Last Hit.
Play safe.
Dont chase.
Ward dragon(early game) and Baron(late game)
Steal theyr jungle buffs if possible.
Save your mana.