Hello there! Welcome to my Attack Damage Evelynn guide.
The hardest thing to play Eve is situation when the enemies have oracle. Most Evelynns I see just stay back in these situations and do nothing, "because they see me". So what? They see our Annie/Garen/Janna/Urgot/Zilean/whoever too. And they do not stay back. Why the hell you do then?
Element of suprise, you say. You want to catch an enemy when he doesn't expect it. OK, just turn on your Ghost spell and ultimate and get him. Oracle has pretty small range, it WILL be suprise, seeing Eve appearing from nowhere with deadly movement speed and killing unexpecting man. Even if he sees you in that fraction of a second, he won't be able to react.
And what if they use wards? Simple - YOU buy oracle and have a nice trip through the entire map, destroying them.

Let's have a look at skills:
Determined Killer (passive) - Pretty useless, but can save your life in some situations, especially in early game while ganking unexpecting enemies close to minions.
Hate Spike - Low damage, but cool to increase damage with Sheen/Triforce every 2 seconds. Get first rank of it when you buy Sheen, rest ranks at the end. Higher ranks at lower levels waste too much mana, and damage is low anyway.
Shadow Walk - Maximize it as fast as possible. Stealth and stun are Eve's greatest advantages.
Ravage - Useless on AD Eve? No! It descreases target's armor, so with armor penetration runes, Ravage debuff, Youmuu's and later Black Cleaver you will ignore their defenses, not only, but they will probably have minus armor. That means additional damage. Ravage also decreases magic resistance, what is useful to your teammates.
Malice and Spite (ultimate) - Cool ulti. Awesome movement and attack speed along with Youmuu's Ghostblade. After buff, you can use it whenever you want. Don't forget to turn it on together with Youmuu's.


Okay, but what with summoner spells?
I think that mobility is really important when you play Eve, because if you want suprise someone who has got oracle, you need big movement speed. So
Ghost and/or
Flash are really good. After patch Flash does not break stealth so it's very useful in chasing. Another spell I like to pick is
Exhaust. It's really good when you want to solo some melee dps, like Trynda, Akali or Yi - they won't hurt you for a few seconds. Another good pick is
Ignite, you know why. It's useless only on Soraka, probably.