Ezreal is the champ i play the most because i feel best when i play him. Im not the best with him nor is he the champ i play the best. But i have the most fun playing him.

I Aim to deal damage with Ezreal so i go 21 in the offensive tree DURR. I also like to survive longer so i take 9 in the defense. Remember that Ezreal has shorter range on his Auto-Attacks than other Ranged Carries.

I get 7 Damage runes and 2 Armor Penetration Runes on Red, Why you ask, im not sure i answer. Maybe i have played millions of millions of games and have tweaked every little bit of this build until i found perfection, but more likely because i get 20 damage in the beginning with the 7 damage runes, and i like round numbers like 20 and Ezreal has a 50 base damage at level 1 if im not mistaken which is also a nice round number and i dont want to ruin it.
The smarter thing would probably be to get full Armor Penetration but i wont be doing that any time soon.

Yellow Mana Regen to afford using my abilities, this will let me last hit with Q and use E to flash over enemy minions and unleash a flurry of Q's and Auto Attacks on enemy champions, they deserve it those bastards.

Magic Resist on Blues because i dont like mages, they are D-Bags.

Quints is for Armor Penetration, with the 10 from quints plus the 9 from Red and Masteris you have, you guessed it 19 armor penetration. This is enough to deal full damage to minions and low armor champs such as D-Bags.

Doran's items are the best to start with unless you want to build a Gold per Second item or jungle(IMHO)

Get a Doran's Blade because it looks cool, its like red and...yeah
It gives damage so you can scare away champions or kill them.

It gives you Health so you dont die, which is a bad thing in League of Legends.

It gives Lifesteal, not a whole lot but it gives you some and you get some Hp regen from masteries. Well you should be able to stay alive a bit longer and not have to recall as soon as you get hit by a spell.

After Doran's Blade you could get another Doran's blade or Brown Shoes. After shoes you get a Tear.
Then you complete Manamune (du du duduru)
Then you get Tier 2 Shoes, I usually get CDR boots but i have gotten Thready Mercury and the Silver Move Super Fast Shoes in a couple of games, IT WORKS

After Tier 2 Shoes and Manamune (du duru du) i get Banshee's Veil, Sheen and Last Whisper in no particular order.

Then i finish of by selling the last Doran's Blade to get Phage and finally Trinity Force which is like my favorite item.

Then if theres time i get Infinity Edge or some other damage item such as Bloodthirster or Hextech Gunblade or maybe even a Bloodrazor.

I take Flash because i like getting away or on some rare occasions getting a Q or Auto Attack in to get a kll.

I use Exhaust to be able to kite Melee attackers better or to slow a champ down so my team can take take that bastard down.

I usually take mid or sometimes bot, and i play offensive.

I deal heavy damage at level 1 so i try to hit my opponent/s hard with my Q

If they play clever and try to hide behind their melee minions you just Auto Attack that sucker in the face, if they stay put you attack them some more. If they back away you try to hit them with Q and lasthit minions. If they try to go after you you E back and Punch them in the jaw with your Fat Gold Ring, that or your Q.

FARM

Stand back in team fights and use your ulti if you think you can hit some of them, then you use your Q and when they are low you finish them of with your Auto Attacks.