Hi, I'm alphaMJL, an Eveylnn fan, and I have created this Eve support build.
I have played Eve for years, in countless games even back when she was consider "troll." I have played her in every position and this is my final frontier with her. I worked on this build for months in team builder(A great place to try new ideas.) I have created this build and guide because I love playing Eve.

Eve Support is a high skill position. You must have become proficient in fighting, engaging and disengaging with Eve and you must know her fights well as you will be playing her very aggressively. Also, in order to be effective in this role, you will need to understand trading and going crazy on the other team if they look at your ADC/Fellow bot wrong. If you use your W to RUN and never look back if they jump you, you will fail here.

You must be a ruthless, crazy, killing machine, ready to die for your ADC. And you must be able to be strong vs those that will tell you that Eve cannot support. You answer only to your duty.

LANING PHASE: Eve provides high damage harass, and pressure with stealth. What she lacks in CC is made up with damage and the constant fear that Eve will appear.

MID GAME: Eve becomes a nimble tanky-ish stealth bodyguard constantly confusing the other team as to how many they are about to engage. Even if she is absent, they may assume she is there, perhaps tilting the favor.

LATE GAME: Eve becomes a screaming fast tank with moderate damage, high threat and continued confusion of the enemy team.

Atk Damage Quints and Reds for sheen, and flat MR Blues because the first 6 levels are the most important to DOMINATE! Armor yellows are standard.

These masteries will balance damage and tankiness which you will need to survive laining.

Level 1 start with Q. You will not be super aggressive with just Q, though you can do some counter trades or initiate some trades on occasion.
Level 2 brings E and now you can really chunk in trades, but still 3 is where the fun begins.
Level 3 and now you have W and you will be able to sprint in and out of trades.
Level 4 Another E. Two Es to start as this makes you burst pretty scary, but after this we will max Q as two in E is enough for laning.

In Summary. Q then E then W. Another E. Max Q, Max E, Max W and of course ULT takes priority.

Flash is needed for disengage and engage.
Exhaust is needed for team-fighting and as a bit of CC which Eve is lacking at first. (Later she will have her Ult and Frost Queen's Claim)

This is a fairly cheap build which will make you ultrafast and tanky with good damage due to on hit from Sheen/Trinity and Deadman's Plate

The order is not set in stone. Sometime you will have enough for pieces here and there. Sometimes you will want wards first, and other times you will want sheen first.

Sometimes you will want the trinity force first and other times, Deadman's Plate.

With Sheen you gain a large power spike.

Buy potions as needed for laning so that you can stay aggressive.

Last item you have many options.
Zonya - Lets you survive ultra high burst comps
Rylai - Fast comps that are constanly kiting.
Liandi - Tanky comps so that you can burn through their hit points
Banshee's - High AP damage comps
Thornmail - high AD damage comps

Be flexible. Buy what you need to get you through your next objective.

Switch from jumping from the bush, the middle of the creep and from the top of the lane. The enemy will often waste skill shots trying to flush you out. It is going to be hit run stealth, change position and repeat. Your E will let you rapidly use all your gold-making charges from your Spelltheif's edge.

Wait til 3 to really get your hit and runs cooking, but you can still effectively trade and all in before that depending on the situation. At 3 your aggressiveness spikes. If you get someone to 2 bars around level 3 or 4, you can often Flash E, auto atk, Q, W auto attack Q. If they didn't flash or CC you, they are likely dead. Level 4-5 your burst will be very nice compared to most bottom comps.

Wait for cooldowns to strike. For example, wait for Thresh to miss a hook and strike. Wait for Morgana to miss a root and strike, wait for Sona to Valor and strike. Try to wait for CCs to be on cooldown. If not, you may hit, but not be able to run. After blitz misses a hook, you have more than 10 seconds to just beat him senseless. This will help on ANY support you play.

You will be warding, playing bodyguard to the ADC or team. Stay stealthed as much as possible, but push a lane if no one is around and it needs to be done. It is not necessary to farm, but you can for lane pressure or to snag a lonely jungle camp.

You will want to stay stealthed so when an enemy team tries to do a 2v2 and they didn't see you, they get the surprise that it was really a 3v2. This will often make the team hesitate to engage.

You will be playing Eve a lot more like an assassin in mid game. This means you wait till some CC and skills are on cool-down and then go in, as you will not be extremely tanky. This will change late game, when you will go in first and get pounded on so your team doesn't have to.

You will be doing the same things as the mid game but now you are tanky enough to be starting fights and you will be focused. At this point the enemy team has had about enough of you and will gladly pour all their damage into your 6khps with shield, too bad they will be on cool-down vs your team. You will have insane speed with your banana boots/deadman, W and flash which can lead to some epic engages.

You will be tanking towers and leading your team to objectives to close the game. Ward the jungles to light up objective paths ward and deward baron/dragon and chokepoints.

This is a very fun way to play Eve. This guide does not cover advanced Eve tactics which I might go into if there is interest. This is more of an intro for those that want to try something new but know a bit about playing support and/or Eveylnn. Please leave questions as I will be happy to update with more info if there is interest. Feel free to contact me in game if you wanna chat about Eveylnn (not during a game please!)

Have fun, and don't be upset if others don't understand Eve support.

"NO BUILD WAS META BEFORE IT WAS META" (Try new things, maybe you will discover the build used on the next championship.) -alphaMJL NA