Now, it's fairly likely that most (if not all) of you have played the old Evelynn, and that by reading this guide you probably just picked her in champion select looking for the right guide.
This is the right guide.
However, I've always felt like jungle Evelynn was weak and there were better picks, especially in the current era. I will not cover jungling in this guide because essentially if you jungle with Evelynn, it will either come to you naturally or you'll be horrible. (most likely option 2)
SO I'm here to help by suggesting that you do not jungle with Evelynn.

I've played about ~100 matches in unranked with the old Evelynn, and I can whole-heartedly say that while her stealth isn't as "stealthy" as it used to be, Evelynn is much stronger than she used to be and can dominate most if not all team fights, even other AD carries with relative ease now.

So without further adue, here is my Hybrid Evelynn carry guide, for any lane but solo top or the jungle.

They're kind of important if you're playing pre-mades/ranked but to keep this simple and sweet and since we're not including my jungle guide just follow my current runes(flat mpen quints and marks, mana regen/level seals, and AP/level glyphs) and you won't have any problems with getting penta kills. I myself don't even have a full tier 3 rune page, (yeah, I know, give me some more grief) but I believe a knowledge of the skills will take you farther than a rune page will. Rune pages are icing on the cake, not the flour in the dough.

Flash: Always get it. It's a great escape, distance closer, etc. If you don't have Flash, you're at a disadvantage if someone else does.

Ignite: Not super important late game, but it helps you get valuable kills in early game, which is really nice and in my opinion is with the sacrifice of having a some-what useless late game summoner spell, compared to other late game ones she could be taking.

Ghost: Really fun, actually. Nothing like having 700 MS for 3 seconds and being able to catch even a Yi with R+ ghost, or dive a tower and leave with only one shot on you, frankly.

Exhaust: Works well with Evelynn's ulti but the range isn't good enough to be of a lot of use unless you use it before they try to run on you. Don't get me wrong -- it can seriously lock someone in place and secure a kill. But I'd rather take Ignite because it seems to work better. (UNLESS you take a point out of the spell vamp and put it into summoner's wrath. In which case, Exhaust is a much better choice. )

I can't really give an honest opinion about the other summoner spells, I don't really use them unless I'm playing support.

For items I obviously prefer an early Doran's Ring and Sheen, -even if going mid- since it gives you that much more power that early and can surprise your opponents or potential fail junglers who think you're an easy catch. I recently tried the regular boots+pots setup last night with a friend who had seen this guide, building the boots before sheen. It works just as good and it's really not an issue. It's just a matter of preference really. IF you think you might be laning against Vayne or some other non skill-shot based champion with a ranged attack, it's safer to buy boots and pots first, and build DRing second so you have a bit more sustain in the lane early on.

After that I usually build Boots, Mobility Boots and Zeal because it brings some nice AS, MS, and AD to the table early on thatcan scale nicely with your E while taking down turrets, gives you a lot of speed for easier ganks and escapes, and makes it easier to dodge skillshots.

Then I start working on Guinsoo's Rageblade and Trinity Force, since they give me even more AS and extra damage when I crit. along with some nice hp, mana, and more movement speed.

If the game's still dragging on, I buy Madred's Bloodrazor for the 25 armor and the unique passive giving me %4 more of their hp damage per attack, which is really nice.

At endgame I buy Malady, since it's even more AS, followed up by Bloodthirster, based on gold available and whether or not the other team is building MR. If you're going against tanky champs/see them building MR, take Malady for extra MR shredding, since it's important like that.

This Evelynn is really quite good if used properly. She really shines as a Mid champ, and it's not too hard to nab farm with her Q if you do it right. Essentially this new Evelynn is very hard to deny farm from, due to her passive invisibility and her Q's range/ AOE effect.

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Shadow Walk This passive is really helpful and while her stealth doesn't bring as much to the table as it used to it is still very viable for scouting areas, avoiding sight with the enemy, and making ganks.

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Hate SpikeUse this to harass, farm creeps, and chase the noobs you deserve to kill, we max this first because it is our main damage dealer, means of procing Sheen and Trinity Force, and works very well for getting those creeps in you are starting to get denied farm.

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Her Dark Frenzy is a godsend, and frankly is something I use to escape and chase. Words of wisdom, don't waste it on an Ashe spamming ice arrows, or any other champ that can reapply constant cc, as the effect is reapplied if you're hit a 2nd time. Her W also gives Evelynn bonus movement speed, so if you're making a getaway, spam that Q, and hit W! We take a point in W early and max it last because it's not very necessary until late-game.

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Her Ravage is basically a weaker, longer CD version of Ezreal's Q that requires melee distance and gives you a hell of a lot of AS. I like to use it once on a creep, then focus a tower with the extra AS just to make it go down quicker, while spamming Q to hold back minions. This works as early as level 2, but is truly effective at level 17. when you have 120% AS, and almost/ more than 2.5 attacks/second. We max this second for extra AS and damage during ganks.

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The ultimate, Agony's Embrace, has many uses. It instantly deals ~30% of the enemy's HP, has a decent AOE slow of 70% and gives you a shield of 300 hp per champion hit. With the CD masteries we take, this baby only has a 66 second CD, making a somewhat safe ultimate to waste, use for escapes, etc. IF you hit all 5 champs, and they're all half hp, they're now 25% hp and you can spam to your liking for a quadra, penta etc. while under the safety of a 1500 hp shield for six whole seconds. If you use this in a team fight and aren't focused down fast, or at all, consider it a victory. We obviously take this one whenever it's up, at 6/11/16.

I like to play a somewhat aggressive Evelynn because I think she brings more to the table than one that plays conservatively, and since many now consider her to be an Ad Bruiser/carry of sorts, it is best to go any lane where you will not be struggling for farm.

As opposed to the old Evelynn, this new one is more Item dependent and thus needs a some-what good creep score to do well. Roaming is also not a bad idea to do early, since Evelynn's Hate Spike can farm minions really quickly if you positions yourself so that her Hate Spike hits all of a majority of the minions in the wave.

Try not to go toe to toe with other champions until you have Sheen because otherwise you will have a hard time escaping or will have to B because you've lost too much hp in a fight. Evelynn's R is her main source of survivability apart from any tanky items you choose to buy, so do not jump into places where you are at a disadvantage(such as a 1v2) unless you have your ultimate up.

This all sounds like simple logic but her ultimate really only makes her the equivalent of Garen in hp in late game. So if you think your (insert 3700 hp champ here) would have trouble in that fight, odds are that Evelynn isn't going to do any better.

Team work is essential to winning games.
If you make a mistake, acknowledge it. If you insult someone, apologize. And if you start doing bad, do yourself a favor and go farm creeps instead of trying to gank or kill champions.

Ping when you are going to gank and tell them you are ,"omw X lane" This lets them know you are coming and lets them react accordingly.
Ganking is kind of nice to do if you see someone on low hp, and is worth it if your match-up is pushing you hard/ has a lot of CC, like Ashe. Ganks are often really easy and safe to pull of with Evelynn if you go mid lane and just wait for the enemy to overextend in Top/Bot. Don't let your team be a bunch of *******, and if they don't wanna fight just start sitting back a little and heading in mid-fight for best results. It's not worth your KD or one kill to be sitting around for a minute watching your teammates struggle.
If your teammates are unwilling to fight, don't accuse them of it, as it will only make them do worse one way or another. If they are doing bad you probably got stuck on a bad team, and unless you premake a team, that's life. Make the most of what you got and you can usually do pretty good.

If someone else wants mid don't make your wrath known, just pick a different lane.
Teamwork wins games, arguing does not.

So that's my hybrid Evelynn guide, and I hope you all enjoyed! If you guys have any questions or concerns, feel free to comment, rate, add me in game Laser Mag, (NA server) and even watch me play. My ELO isn't very good because I started the second I turned level 30 and didn't have any runes/champs/experience at all, so don't judge. I try not to play ranked because more often than not I spend more time in a queue than actually playing, only to be trolled or raged by someone, and that's not what I intend to spend my free time doing. Thus most if not all of my games are Normals. Thanks for reading, and I hope you guys enjoyed my guide! It was my first.More wins to come. Good luck, and enjoy the new Evelynn!