Hello,
This is my first post/build/guide/rant/walloftext and anything else you might want to call it. My main inspiration for creating this build is for the reason that everyone I see playing eve suck's. They build horrible build's and dont utilise any of Eve's nuking potential and prefer to use her as a sort of damage dealer with very little survivability.
It basicly ends up with a 3-10 eve who really did nothing all game.

Still editing, no downvote's till i fix it plawx.

Pro's,
Fairly easy to play,
Super strong nuke,
Great ganker,
OP.
Can shut down anyone in the game with combo at late game.

Con's,
Focused all game,
Does'nt do much after ult and dfg combo,
Squishy as hell
Easily shut down by anyone with consistent damage
Requires alot of hp pots.
Everyone QQ's that you will suck.

Basic caster set up.
Magic pen is always good

Mana is really only needed for really early start up as sometimes you have no choice but to farm with q and wait for ganks, and you really need to harass with your q aswell.

Cdr is becuase Eve's ult has the worst cooldown for an ap caster and you're almost useless without it.

And qp quints becuase well... you know.

Basic caster masteries aswell,

Dont really need the mana regen past 12-15 mins. Movement speed is always needed.

Boots
Health Potion x 3
Basicly the only way you can farm and harass and gank.
Sorcerer's Shoes
So you can escape, juke, kite, gank, hurt, and be everything you ever wanted to be.
kage's lucky pick
A little extra gold before you pickup dfg.
Deathfire Grasp
op nuke, get this asap.
Haunting Guise
sort of a toss up between dfg and this first great item to get in most cases generally ends up with you doing true damage to squishies.
Athene's Unholy Grail
no mana problems ever. gets your cdr too %39.67 helps against counter nukes.
Rabadon's Deathcap
op.
Lich Bane
dem auto attack's.
Void Staff
What's a tank?

Flash gap closer/escape/op.
Ignite extra damage/anti heal. Basicly stop's healer's from living if they manage to survive your initial nuke.

Max hate spike, then ravage, then dark frenzy, whilst leveling ult at 6-11-16.

Ganking, get into position close in as soon as they get sight of you cast w for gap closer, dfg/r/q/e/q/q/q/q/q/e/q/q/q/q/q....etc.

Team fights, Get into position and never ever ever ever go in first, Find the highest priority target, such as someone who can lock your team down or the person with the most kill's or most damage, Generally a bad idea to focus tanky people without a void staff unless they build alot of hp and have low mr.

How to turn a game into a 4 v 5, wait for someone nukable to get out of position, come out of freaking nowhere cast everything you have and w back out, very dangerous all or nothing kind of move but works well when you know what you are doing and who is easy to nuke.

In team fight's wait for someone on your team to get focused, run in and nuke the squishiest person standing next to the most people, as long as your doing all right in farm and kills you should be able to imediatly kill one and have a strong enough shield to survive the damage while your team comes in and steam rolls them.

Basicly your goal in game is to shut down anyone with the most damage or the biggest threat to your team, Anyone who over extend's should die, ward control is a must with eve, if they know where you are, you cant do anything.

Eve is countered by alot of people, generally I go mid lane but if it's someone I cant lane against like, vlad, ryze, akali. or generally all ad char's. If i can only farm in lane I just go into stealth and run off to a lane with someone pushing and get some kills in that lane.