Hello, this is my evelynn guide. Although many people play her jungle or just plain roaming in this edition of her i play her bottom. I do so to let her get the proper exp without lagging behind, while still having ample opportunity to get kills and gold. Although she won't be getting CS there are many options one has.

The reason i chose these runes are simple, the magic penetration to get that little umph to her damage, the armor runes to give her a little sustain and make it so she doesn't take as much damage. The gold p/s is to get that extra gold in she will inevitably lose from lack of cs.
Then the glyphs for MR is to ensure nuking doesn't do as much of her health as possible and to give her that little boost in lane. And the quints are to boost her E and give her extra damage.

The masteries i chose were to get the most AP i could while not having to commit that much to it with items and still having enough to make her Q and E useful, while still making her do decent damage with auto attack. Then the extra AM and MR to help with sustain in lane and to avoid taking too many big hits.

Now the items i chose my seem odd and are open to variation in the order taken, but essentially those can be the optimal items for Evelynn.
Starting off with boots and 3 pots, standard start up gives her the ms she needs to utilize her W to slow and keep attacking. Now the Mejai's for me works best with the way i play her and get certain amounts of ensured kills or assists per game but can be swapped out for Deathcapp, or Void Staff for that extra penetration. Now depending if you get Mejai's rushing GA afterwards to ensure you keep all your stacks and don't die is very helpful(note only do so if you get a good amount of stacks that will keep you putting out enough AP damage). If you do get GA then you should be participating in fights more openly so you can get either kills quicker or assists +gold so you can farm sheen, then trinity to get some real damage.
Afterwards, going madred's or Bt is just a matter of opinion, i prefer madred's for the extra damage+ as combo thats good to get those last bits of health off crunchy champs.


Now for the second build it is a slower start with some more damage late game and has a real snow ball effect, starting with some regen it makes going invis and hitting them much easier to recover from, and since you also start with a ward you can also keep form getting ganked.Now again i rush the boots of mobility right afterwards to have that extra mas to chase someone if invis in persuit, or to get away from someone if i manage to invis, then the MS stacks as i run and i'm sure to get a clean get away. Then the Kage's pick is to allow for small AP while still more gold income until you obtain Sheen/Wriggles which ever is more beneficial to your scenario. Then after that the build is almost similar with the acception of void staff, since its such a late build, or build up void staff seemed more appropriate at that period in the game seeing as kills might not be as easy to come by.

Ignite to get that last bit of HP on someone, or to keep an enemy tank from regenerating crazy amounts of hp, and flash for escape or catching someone.

This evelynn build is a snowballing build that might not prove too well early game depending on how your mejai stacks, and whether you decide to get more survivability from GA or the extra damage output from trinity.