Hello Readers my Name is Huntermanone my online friends Call me Arnie this is my first guide so i hope you enjoy it let me no what you think.
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Pros:
+ Great Burst and Assassin
+ Great Gank Power
+ Quick Escape
+ Gets feeded rather quickly and works with pretty much any team
Cons:
- Squishy
- Tends to get focused in team fights

Jungler-
In early game if the enemy team have a Jungler invade their camp if it is a Jungler with Mana likely odds they are going to the ancient Golem, if it is a Jungler without Mana E.G. Lee Sin or Rengar they will be starting off at the Elder Lizard, inform your team mates that you are going for a Gank and then they might be willing to help you, Wait for the Jungler to open up on the Buff giving monster then run into the pack try to steal the buff if possible if not continue doing damage to them and pick up an early kill.

No Jungler-
If they have no Jungler their are a few things you are able to do you can either stay in your lane and wait for level 3 to get a kill on the champion in your lane or you can go and help either the bottom or top lane for an early kill witch will be able to push that lane.

Figuring out which to do is not hard if your team has a Jungler and a solo top champion pull the monster for him and head to top lane for a early game kill or assist, if both lanes are occupied and you have no jungler you can take your pic of the two lanes to help out.

Boots of speed + 3 health potions:-
Its always good to start a game as Evelynn with the movement speed so you can get to enemy lanes or jungles for early kills, starting early game fights with a health potion before jumping in is a good way to increase survive-abilty
Kages lucky pick-
This is a good early game item to take as it gives AP (Ability Power) and extra gold during Game play this will then later be upgraded into a Morello's or sold back to the shop
Hextech Revolver-
I choose a Hextech Revolver as an early game item as it provides you with extra AP and some life Steal through Spell Vamp
Sorcerers Shoes-(with Homegaurd Aura)
I choose these shoes as playing Evelynn with magic pen runes the extra magic penetration will increase your damage output,Get the Home Guard aura at the end as you do not need to waste the gold buying this item until it is the very last item to buy.
Ice-born Gauntlet-
The ice born Gauntlet is a new item addition to league of legends it provides Evelynn with bonus Damage through sheen and the AP from the item as Well as Armour for more survive ability, the Mana bonus and cooldown reduction allows Hate spike to be Cast more Frequent.
Morello's or Rabadons-
For this item choice it is completely down to how the game is going.
If you find that you want to cast your Q more frequent take Morellos for the extra cooldown reduction, also Morello's is a good item to have if the enemy have a healing Support champion as it reduces the targets healing and regeneration by Half.

If you find the your damage output is not as high and you are losing fights take Rabadons instead as it provides you with more AP( Ability Power ) to have the use of for extra damage.
Crystal Scepter Or Void Staff
Finding out that enemy's are getting away quicker take Crystal Scepter to slow them down, the Scepter provides a good slow a decent amount of AP for damage and extra health to increase your survive-ability.

Finding that your damage is lacking Grab the void staff for more Magic pen and Extra damage against champions.
Frozen heart or Guardian's angel
When in fights if your find your Mana is going to easily and your opponents are too Squishy and get away Take the frozen heart.

To better improve your Survive-ability in game i suggest taking the guardian angel as it provides you with bonus Armour, resistance and also revives you if you die.

Any variation of the items is possible and will work.

Marks
Magic Pen: these marks will provide you with more damage against champions with Armor and increase damage on those with low Armor.
Seals
Cool-down: these will make Evelynn's Ravage to be used more often, as well as Reducing the cool-down of your R ability.
Glyph's
Cool-down: These will make Evelynn's Ravage to be used more often, as well as Reducing the cool-down of your R ability.
Magic Pen: These will provide you with more damage against champions with Armor and increase damage on those with low Armor.
Ability Power: This will Give you more Damage out-put
Quints
Ability Power: This will Give you more Damage out-put

Offence Mastery
When picking this mastery set-up it is important that you focus on Damage, Ability Power and Cool-down Reduction that is why i choose this set-up.
Utility Mastery
For this mastery i focused on Giving Evelynn Extra Mana and cool-down reduction so you are able to focus more Damage items

I recommend taking hate spike first and maxing it first; then take Ravage followed by DF Max Ravage by level 13, maxing DF last, level up your Ultimate ability at level 6, 11 and 16
Shadow Walk : Her Passive. Good for roaming and walking around wards, gank undetected (unless they have a pink ward) and place wards without being seen. Pretty good if you ask me!
Hate Spike (Q) : Ah, very nice ability. It lets you farm from afar, finish off kills that are out of auto-attack range. It should be your priority spell and you should spam it whenever you are chasing someone or assisting in kills. Even when being chased, throw some spikes back at them, who knows, maybe they get scared or you drop them low enough to be!
Dark Frenzy (W) : Best thing about this skill: 0 Mana Cost! Great to spam! Spam it when you are going to lane, spam it to get the kill, its really good for Eve. It basically makes her Kiting ability even better. Get the kill then run.
Ravage (E) : Another ability that I personally, just love! Killing becomes easier when Ravage is used. It does nice damage, it makes Evelynn attack faster and makes her kit even better. Tip: when taking down a turret, i recommend you to use Ravage on a minion to gain extra Attack-Speed
Agony's Embrace (R) : very useful ultimate. Every combo needs or should start with this spell. You slow down the enemy, take the bonus health (in team-fights i suggest to hit as many targets as possible to make the shied even greater) throw DF or a flash E then Q if needed. Or when battling 1 vs 1 use it in the last moment or close to the end to surprise the enemy. They wont even know what hit them!

If you found someone alone or gank a lane where he is alone use the following combo: Agony's Embrace > Ravage > Hate Spike . This should nuke the enemy target and you will eventually get a kill.

General farming and Champion Ganking
Farming as Evelynn is easy peasy lemon Squeezey
all you need to do is take note of her passive.
Shadow Walk- Prioritize's previous enemy hit for Evelynn's ability
this is good when farming minions as you can hit one of them line them up and continually cast your hate spike for damage on minions.
Mid - Late game farming-
Taking the Golem and/or lizard buff is a good way to keep mana up and get a good constant supply of damage to champions
You can also farm Wraiths, Dogs and Golem's for bonus gold at level 13+ you can solo dragon for an extra pile of cash

Melee Opponents
When fighting melee opponents try to get off your R first then open with a ravage and begin a rotation of ravage and hate spike for extra damage to catch up to them when they are running use W alternatively to run away.
Ranged / Spell casters
When fighting spell casters or range be aware they are squishy and can get away so it is important that you save your R and W for a chase fight seeing them get away you can quickly use dark frenzy to catch up followed by an Agony's embrace for an impale and a health shield to ensure survive-ability.

Now you should at least have a kill or assist. Go back to your lane and start to poke more, put more pressure on the other AP. Gank again! This time you will only be more powerful, right? Keep doing this till you feel like the other team-mates don't need your help anymore and start to focus on pushing mid and killing the other Mid Champ.

Also don't forget that Eve's passive does not fade off when you ward, use HP pot or activate Oracle's elixir, Grab 2-3 wards and put them in the enemy jungle or double ward mid just to be safe from a jungler or potential Gank.

Team-fights should start now, at least little battles like 4vs3 or 3vs3. Always focus the squishy! Focus the Carry or the Mid depending on the champion (If you have someone like Corki you are going to focus the AP, and if you have someone like Gragas of course you are going to focus the AD) or even focus the support! A kill is a kill. You need to get out of the fight pretty quickly because the focus will turn right on you after you start hitting the squishy targets.

You and your team should focus on The Elite Monster's, Dragon and Baron control are a must and you shouldn't roam so much now, not without wards or at least some visibility. Again your role is to melt down the AD/AP and then let your team go on from then. Of course if you finish either of them you gotta jump down on the other as quickly as possible. Remember, stay safe and walk around until you found the opening to attack.

Push your lane, destroy turrets, take Baron quickly if possible and always be safe. Take an oracle and start to roam with a Partner, Don't forget that not only the Support takes wards, but the whole team, including you.

Top lane:

Believe it or not Evelynn is a Great Solo top lane Champion, As she is an amazing harasser Jumping in a game with a friend who is a jungler is a good way to seize domination on top with your partner coming in for a gank Evelynn can wait for the team mate to set up the route of kill position jump in with the use of flash and dark frenzy followed by ravage and constant use of hate spike.
Good jungle partners:-)
Lee Sin, Rengar and Warwick.

Evelynn is a great AP champion being a squishy target she is amazing in mid lane she has many different Variations of play so when building a team make sure you take that into account, she is a great harasser of a lane being able to Stealth and Regen mana allows her to stay in lane longer then her opponent's.

Thank you for Reading My Guide :)