Soulstealer is also a posibillity early game.
If you gonna go with soulstealer just buy it after boots and then buy the items in the same order, sheen, lich bane etc.

The most important thing to Remember with evelynn are that she is made to walk fast between the lanes and gang enemies. In 5v5 don't always use the path with water, walk in between the neutral minions in stealth.

Awareness is key, early and later game. Keep track of your enemies, see if they put out Wards, or if they organize well. Keep track of those low on HP, and if they are ballsy or just blatantly ignorant to their own HP. Control over the map and your enemies gives you the edge.

Start off by focusing on last hitting minions, and sneak in some harassing here and there.
At this stage you maybe not be able to bring anyone down, if you have the shot try but don't play stupid. Focus on keeping their HP lowered till later.

Around mid-game you'll probably landed some kills/assists (because of early harassing, and some neat use of Ignite), got some items, and you're half-way there to become a mean-killing-machine.

If you are so far that you got Deathfire it's time to head out ganking. It's a great opening item followed by a Ravage, and it will utterly devastate your enemy (even tanks).

If the team is packing Oracle, and putting out Wards all over the place, make good use of the bushes. Even though your stealth is half-way disabled, you can still make good use of the bushes, and somewhat get your element of surprise back. And Remember when you comes out of stealth and attack you stun your enemies.

If you see the team placing out wards, or you KNOW they are using them; Buy an Oracle Potion for yourself. You can then see their wards! Kill 'em, and get on with your life.

If the team is packing Oracle, be my guest, use stealth.
But only when the opposite team is preoccupied with one of your teammates.
They are either to busy with your teammate, or just don't see you.
Land the stun and get yourself a kill!

After that... Just go for it, enjoy, but don't get ballsy. It will be your undoing.

If you enimies set wards buy oracles.

Summoner spells:
Ignite is good to damage and reduce heal if other have heal or against mundo. exhaust is ulti nice cause the blind 100% miss, and slow open battle with that after ravage.

Runes:
The reason why i have chosen theese runes is because you start with about 100 more hp in lvl 1 and they just layed back AP and attack damage/speed. attack damage and speed is good because of your lifesteal and of course more damage. early game and a bit late game you need mana with Eve, therefor mana runes.

Masteries:
It's very important to get reduction on your exhaust and ignite and improve them they are very importen when you come out of stealth and attack.

Abillities:
It's important to take shadow walk and ravage first if you want kills fast, hate spike is very good to last hit and kill minions.

Items:
it's important that you can move fast between lanes in stealth, and when you enter shadow walk you lich bane is activated you will damage alot better when you comes and suprice your enimies. It's important to spam you hate spikes now when you have spell vamp, you can get up to 40 life per spike and every time you use it there will come 2 spikes.

Early game:
Just get your XP last hit minons with hate spike, if there is an opportunity go for it, if you have a tank like rammus or shen who can taunt you have a good shot. If a kill not is possible go shadow walk and be in "xp-distance".

Mid game:
Start ganging, it's very important to get some easy kill by helping out in the other lanes, when you are in other lanes and you can see alot of minions in a line without any players go there and kill the minions you are proberly the one with fewest minions killed.

Late game:
This is the part where eve rape, move in stealth between the lanes and just kill them come out of stealth open the battle with ravage, deathfire grasp, ultimate, and then just spam hate spikes. And if they focus you, use zhonya's ring.

Hate spike:
I can say almost pretty sure that hate spike is one of your most important abillities. Nearly no mana cost, and a lot of damage and life steal with this build. Hate spikes are also good to push and kill minions, and last hit minions, when you are in combat or team fight always spam hate spikes no matter what.

Shadow walk:
Shadow walk are very important. you can use it to scout with to get firstblood, and scout later in game. Shadow walk is the ultimate abillity to gang and get kills just stand behind then in shadow walk and wait for the right time.

Ravage:
Ravage is your open abillity always use it to start combat with, it's your best damaging abillity. it's the primary damage abillity.

Malice and spite:
Malice and spite always use it in combat no matter what if you get a kill cooldown will vanish. the passive does that if you kill someone you restores life. This abillity is also good to escape from enemies with.