This is my first guide so don't judge me. :-) Anyways, I am an Ezreal player and am tired of seeing people build him in such a weird way. He needs Trinity Force in his build or else he just does not work well.

3 life steal quints for that early game stability. 9 greater marks of insight for getting through that little bit of armor that is keeping you from dealing bigger amounts of damage early game. 9 greater seals of strength because you want that attack damage. 9 greater glyph of strength because it gives you a small boost of attack damage but may be changing it to 9 greater glyph of might so that it scales per level which would give more damage overall.

I go 30/0/0 because Ezreal doesn't really need mana regeneration IF you use him correctly, unless if you just feel like pushing a lane and spamming Q at your opponent. Ezreal is a hybrid character so his Q and his R both scale off of Attack Damage and his Ability Power. You will end up getting more AP from the sheen then you thought you had before and your Q does twice as much damage with the Sheen Proc.

I start with 3 Doran blades and boots for early game stability and start selling them off after I build Trinity Force because he gains health from the Phage and you are getting lifesteal from the Wriggle's Lantern. I would then build Bloodthirster after Trinity Force for more damage and the lifesteal and then build Last Whisper for the Armor penetration and AD, then comes the Infinity Edge for the big damage and then the Warmog's Armor when you sell your Wriggle's Lantern. The reason I don't build attack speed items besides the Trinity Force is because he has a built in Attack Speed bonus every time one of his spells hits an enemy and then he can use his W to slow down an opponent's attack speed.

I use Exhaust and Ignite on Ezreal for slowing down my opponent and then dealing damage to them while lowering their heal/lifesteal amount. The reason I don't use flash is because of Ezreal's E because it allows you to either "flash" towards and opponent or "flash" away from an opponent while in a teamfight and your getting targeted.

You usually just auto attack but can use your Q to last hit minions if you can't auto attack 2 minions in time. Buying Wriggle's Lantern also helps because it gives you armor, attack damage, life steal, and the chance to deal extra damage to a minion which could help you push a lane or get some minions hits on a champion if your going aggro.

The reason that I max my W before my E is because Ezreal is laning against another AD carry most of the time so you want to slow down their attack speed as much as possible while you are also gaining attack speed from the spell hitting the opponent.

I hope my reasoning for my skills, runes, mastery tree, and items makes sense and if you have any opinions or want to help out the build at all feel free to comment! :)