Hi there!
I have played a lot of Evelyn games on mid/top/jungle/support lanes. For thi guide i wanted to show you how i build Evelyn as my main mid lane champion. A lot of You may be lost with my items but i will explain everything as clear as i can.

FYI - I'm not writin' this to look nice but to let anyone to know how i play Evelyn.

The reason i play Eve so much is because of her insane mobility. After reaching lvl 4-6 i can roam a lot. I can go counter jungle, gank bot or top - why? Because of her passive stealth and because of her W skill. Another great advantage is her %hp damage dealt from her ultimate (I know it will be nerfed but imho this will not change a lot of my gameplay style). So let's go to the items....

First of all - after last patch boots are not neccesary on start - better buy more potions and crystalline flask to stay on lane and farm more safe on full hp.
First time on base you should buy boots and at least Haunting Guise. Boots for faster roaming over the map and Haunting Guise for HP/Magic Penetration. Blasting wand is next item you want to buy.
Of course what else? If u have advantage on lane with minions/kills and u are roaming a lot, next item will be Rabadon's Deathcap.
If u are having problems with someone (like Ryze, Morde) better invest your money in Giant's Belt for more sustain and durability. If u have gone for Belt you should buy asap Rylai's Scepter.
In that moment ALL players that played with me was flaming me - "WRONG ITEMS, WTF ARE YOU DOIN?!?!"...
Here comes explanation - With Rylai i have a lot of HP, more AP and great passive - my spells SLOWS TARGET SPEED. Why is that so important? Because with Evelyn you can spam Your Q and whenever You are ganking - you will be always the fastest unit!
My core items are Rabadon -> Sorcerers Shoes -> Rylai -> Liandry's Torment -> Guardian Angel -> Abbysal/Warmog/Lich Bane/Zhonya.

The last three choices are just situational items - if your enemy team is dealing more magic dmg take abbysal, if more physical dmg take zhonya, if both are strong - guardian angel, if they are really weak buy Lich Bane and just kill them.