I made this build guide to help out a friend to what makes a good build guide, I'm using his build info but with my view of how to play eve.

Also like usual this is a GUIDE, and everything in league of legends is situational, but it should give you an idea of how to play eve as an AP Carry.

My first build guide so don't know how to add pictures or do any cool stuff

I will not explain the terms like CC and MRes if you need help google has all the answers

Constructive Critism will be nice and maybe a few tips to make my guide look better

THIS GUIDE IS NOT COMPLETED YET!!

So I (as in my friend) have been playing Evelynn since Season 2 up until now,and to be honest, shes a fun champion to play that makes the enemy wonder where you are at all times. I've played her in ranked and shes being banned more often due to her presence in the game, which I will explain in the next few chapters.

Pros

Aoe ult that slows
Mana regen in passive
Stealth
Fun to play
Low cooldown harass
Very flexible in item choices

Cons

Squishy early game
Focused
True sight will shut you down

I deviated from my friends rune page a bit.
I go 21/1/8 because when building eve AP you should be focused on as much damage output as possible,
but you can also change your rune pages and adding a bit more to defense in exchange of utility

Seal of Health: I find evelynn extremely squishy early game and can die from any from of cc or burst

Seal of Mana Regen: Even with her passive she's very mana hungry if you plan on spell-spamming, feel free to replace these with more health seals if you don't plan to use your spells

Quint of Ability Power: More damage output

Mark of MPen: The ability to go through magic resist is essedntial

Glyph of Ability Power: More damage output

I will list all the items that could be used on eve and why you should get them.

Sorcerers Shoes: Your go-to item, you should get this most of the time for shredding past their magic resist

Mercury Treads: For high CC teams and/or high AP teams

Rabadon's Death Cap: Get this when you need a huge damage boost

Zhonyas Hourglass: For AD teams and if youre being focused

Hextech Gunblade: Lifesteal and spellvamp for sustain and damage and if you plan on going hybrid

Abyssal Scepter: For enemies that were smart enough to build magic resist,also you're melee so it has maximum effiecncy

Liandry's Torment: For the high health champs and to give you a bit of sustain, works great with rylais

Rylais Crystal Scepter: For the health if you feel you're to squishy, for champions that have lots of movement speed or escape, works great with liandrys

Will of the Ancients: For the spellvamp if you don't plan on being hybrid, max effiency reached when other teammates are also AP

Lich Bane: More damage output with added speed, handy if you're going to spam spells

Void Staff: Goodbye magic resist

Seraph's Embrace: For if you're a spell-spammer

Athene's Unhonly Grail: For high AP teams and that infinite mana regen

Rod of Ages: For more health and surviability

Guardian Angel: If you're being targeted and need more defense all around

Deathfire Grasp: If you plan on being a glass cannon, dont forget to use the passive!

Frozen Gauntlet: For high AD Team and health, good Aoe effect if you plan on spamming spells

(Passive)Shadow Walk
RANGE: 700

PASSIVE: When out of combat for 6 seconds, Evelynn enters stealth only being able to be seen by enemy champions (within 700 range) or true sight. Evelynn regenerates 1% of her maximum mana every second while stealthed.
Casting spells, taking damage or dealing damage reveals Evelynn for 6 seconds.

Use this as often as possible, if you're out of mana or want to roam, it will make the enemy team have no idea where you are at any given moment, also makes it very easy gank.
MAKE SURE THERE ARE NO VISION WARDS AROUND


(Q)Hate Spike
RANGE: 500
COOLDOWN: 1.5
COST: 16 / 22 / 28 / 34 / 40 mana

ACTIVE: Evelynn fires a line of spikes through a nearby enemy, dealing magic damage to all enemy units in its path.
MAGIC DAMAGE: 40 / 60 / 80 / 100 / 120 (+ 45% AP) (+ 50% Bonus AD)

Generally, max this first because your hate spikes will have a lot of harrass early game and late game, you can also use this to farm and last hit due to its low mana cost and cooldown


(W)Dark Frenzy
COOLDOWN: 15
COST: No cost

PASSIVE: Evelynn's spell hits on enemy champions grant her bonus movement speed for 3 seconds. This effect stacks up to 4 times.
BONUS MOVEMENT SPEED PER STACK: 4 / 8 / 12 / 16 / 20

ACTIVE: Evelynn removes all slows affecting her, gains bonus movement speed for 3 seconds and ignores unit collision. Champion kills and assists refresh Dark Frenzy's cooldown.
BONUS MOVEMENT SPEED: 30% / 4

Use this to escape or chase an enemy as it removes slow debuffs, note that it has no cost so you can spam this, also note that this will put you out of stealth when you activate it.


(E)Ravage
RANGE: 225
COOLDOWN: 9
COST: 50 / 55 / 60 / 65 / 70 mana

ACTIVE: Evelynn slashes a target twice, dealing magic damage with each strike. Evelynn then gains bonus attack speed for 3 seconds.
DAMAGE PER HIT: 35 / 55 / 75 / 95 / 115 (+ 50% AP) (+ 50% Bonus AD)
TOTAL DAMAGE: 70 / 110 / 150 / 190 / 230 (+ 100% AP) (+ 100% Bonus AD)
BONUS ATTACK SPEED: 60% / 75% / 90% / 105% / 120%

This spell isn't that useful when you go full AP, but you can use it in conjunction with your q to do more damage or when you're 1v1-ing someone. This ability can target minions so a good trick is to use ravage on a minion when taking down a tower so you can get more dps on it, maxing your w or e first doesnt really matter if you're going full ap, it depends on your playstyle.


(R)Agony's Embrace
RANGE: 650
COOLDOWN: 150 / 120 / 90
COST: 100 mana

ACTIVE: Evelynn impales all enemy units in target 500-diameter area, dealing magic damage equal to a percentage of their current health and slowing their movement speed for 2 seconds.
Evelynn siphons their pain, gaining a shield that grows in strength for each enemy champion hit and lasts up to 6 seconds.
CURRENT HEALTH TO DAMAGE RATIO: 15% / 20% / 25% (+ 1% per 100 AP)
SHIELD STRENGTH PER CHAMPION HIT: 150 / 225 / 300
MAXIMUM SHIELD STRENGTH: 750 / 1125 / 1500
SLOW: 30% / 50% / 70%

Her Ultimate is still pretty useful even with the recent nerf, it's best used in a teamfight where you can get maximum shield strength and as an engaging tool. Another way it could be used is escaping, if your w is not enough to escape, the slow from your ultimate will help you also giving you a shield.

Early Game: What you should do is continually harrass with you q while also last hitting with it, this might push the lane a bit so make sure you ward, when the lane is pushed feel free to roam around the map to gank cuz eve is a roaming champion.

Mid Game: You should be mostly focused on helping other lanes and pushing out mid, the first teamfights should be fighting, so make sure you're there to engage with your ults, getting some objectives would be a good idea

Late Game: Go do as much damage with your hate spike and stay back before you get focused, if your team can handle a 4v5 then go split push and get some towers for your team, again though, your ultimate is an important asset in a teamfight.

In the chapters above I talked about how you should change the items and masteries depending on your playstyles, if you don't know, there are 2 general ways to play eve.

Fast n Furious

Basically waht you do is stay to put as much damage to the enemies as possible by stayingclose to them, but it's risky

Gun n Run

What you do is stay stealthed and jump in, do as much burst as you can, and when they focus you down, just w away, also very risky

Better safe than sorry

In ARAM you want to max q and w first because if you are ever close enough to use your e, than you'll pretty much be instantly killed, what you should do is stay as stealthy as possible and only engage when neseccary and your not being targeted. It's also a good idea to build tankier and spell vamp for more sustain.
Start off with 2 Dorans Ring, Boots of Speed, and 2 Health Potions.