Pathing

Ideal pathing is into pushing lane that is squishy that opposite of the enemy jungler. We don't want to fight early as evelynn, so avoid enemy jg as much as possible. Idealy we want to path into squishy enemy champions. The easiest to gank are immobile mages on mid lane.

Objectives

Either trade objectives or take them only if you have prio on lanes. Don't contest them 1v1 and don't force them. If enemy takes drake with their bot, don't force fight. You can steal objectives easily in mid/late game, as your ult + smite combo deals 3k+ damage to drake.

Early game

Ward enemy raptors / own banana bush before camps spawn. There are a lot of champs that can go raptors into invade, so beware of those cheeses. You can start raptors if you know that you win 2v2 on mid lane after first clear and you don't want to path to either bot or top lane. Play for camps before lich bane and level 6. Take only guaranteed ganks/fights.

After lich bane

Start to value ganks more than camps. You can force ganks and skip gamps. After level 6 the easiest gank to do is lane gank on bot lane, as most of the time when their adc sees charm on them they go into bushes and their supports stays inbetween river entrance and adc, so it is easy to hit charm on them. But beware of items like ludens and their poke, as it reveals you so the gank fails.

Try to gank opponents without flash. Generally on mid lane it is easier to gank, depending on the champions. Beware that many chamions on top lane can 1 v 2 if they are ahead and the gank is not executed properely.

Try to look for tower dives on bot/top lane, but keep track of enemy mid/jg, because they can easily triple kill you after the dive.

Mid Game

Here you try to avoid teamfights and get picks. Patience is key since there won't be a lot of chances to catch squishies, but with proper positioning it is possible. Try to either kill their back line if they don't have peel for you or defend your own back line from their assasins and bruisers,charming them and oneshotting them. Try to play for sidelane with stronger teammates.

Late game

Late game you do the same as mid game, but you don't have the permission to go for risky plays and picks. Focusing their backline is almost not an option anymore, because you will get oneshotted before you can do anything. Peel for your backline instead.

Your objective steal is extremely good, as your full combo deals more than 3k damage. Hold your flash for stealing or escaping if you have big shutdown on your head. Not worth to waste flash for killing enemies, only if they have big shutdown.

Full Combo

Full charm -> Q -> E -> Ult
Deals the most damage. If you can execute it properly most chamions are dead from this combo.

Early game combos

Q -> E -> Full charm -> spam Q
Combo for early game. You deal burst damage and leave a charm. As evelynn you don't want to fight early, but if you should, this is the combo. Don't start with charm because it is easily escapable. Your E gives you movementspeed in order to escape prolonged AA trades, but you are close enough to hit charm with Q. Don't forget about your autoattacks after the charm, as they deal significant damage early. You can cancel the charm early if the enemy can escape under tower / flash over wall and you beat them without the full charm.

Spacing with Q
A lot of people underestimate the potential of evelynn in spacing. Your Q has a very low cooldown and you can kill many melee chamions early just because they can't get to you. Make sure to save your W when the enemy is running/engaging with ability on you, so you have time to increase the distance between you while they are charmed.

Other combos

Full charm -> Q -> Ult
Good when you pick their backline and they have point and click cc vs you. May be not enough to kill them, but you simply don't have time to get in range for E.

W -> Q -> E
Not waiting for full charm when you don't have time since they are too close to tower/escape.

W -> R backwards -> Hit charm with Q -> E
When enemy is running and you are sure that you oneshot without ult. Leaves you vulnerable, so make sure that the enemy is alone.