~You can run away and cast your hate spike without pausing your movement, very great for getting away ~with a Rylai's Crystal Scepter
~Use your W to get to places quickly.
~Use your Q for minion farm
~In laning phase, since you're going up against a ranged ap use your stealth so you don't get harassed, only use your q for positive exchanges and last hitting minions.
~If low Mana stay invisible, rapid mana regen is very helpful.

~Boots and 3 pots NOT doran's ring. You really don't need doran's ring. Boots for mobility t dodge skills from the APC during laning phase, also mobility is really great on stealthed assasins. HP pots because you will be harrassed due to the fact you're more close distance and they are more ranged.
~CDR is AMAZING so grab the Deathfire Grasp and Frozen Heart... Because you want to be able to spam your Q as much along with your ult... around 40 seconds is your ults cd with these two items.
~ Mobility Boots because you can gank your other lanes faster, yes that is jungler's job but the extra kills will be AMAZING for your all around game.
~ Deathfire Grasp = active, ap, CDR... NUFF SAID
~ Rylai's Crystal Scepter Hp is very good. Also this + your Q = amazing cc, because Evelyn only has her ult for cc. Also... Her Q+ Rylai's Crystal Scepter is amazing for getting away...
~ Frozen Heart, Armor since you will be focusing the carry a lot this will help, plus it's always good to have someone on your team run a Frozen Heart for the 20% AS slow aura, the mana doesn't hurt and the CDR(Cool Down Reduction) on it just makes it eve more necessary.
~Situationals- Rabadon's Deathcap if you need more ap, Void Staff if they are doing not too much damage to you and have MR, Abyssal Mask if they are more AP and have some MR. Guardian Angel, since you will be focused is great because of the passive + armor+ MR. When you get back up, just press W and run...
~The rest... explanitory