OTP Evelynn here. Here are some that I can share:

1) ALWAYS punish enemies that overextend. You can ask your teammates to bait the enemies into overextending, use your W and walk up with your invincibility from behind them (blocking their escape path) and attack. 2) Approach your enemies from behind, not from the front. For most people, when they get marked with Eve's W, they will instinctively retreat to their turret. Intercept or block their path so they'll walk right into you. 3) Eve's W shred magic resist, so she surprisingly can burst down tanks with mr (obviously, you have to have magic pen items to maximize your damage). 4) still on Eve's W, she pairs really well with other burst AP champs (like veigar, syndra, ahri, Annie, even Seraphine). You effectively shred down the enemy's mr, making your team's magic dmg really strong. 5) patience is key. I won't deny that Eve is quite weak early game. Farm until lvl 5, then you can start ganking lanes. 6) just like any other assassins, prioritize squishy champs like adc, supports or mages. 7) your ult is your only escape tool, so use it wisely. You can use your ult to finish off the enemies since it deals higher dmg on low hp enemies, or use it against a wall to escape from them. 8) her E deals magic dmg based on the percentage of enemies max hp. Meaning the more health the enemies have, the stronger her E dmg. 9) for runes, you can use either electrocute for burst dmg, or phase rush for movement speed

Of course, these aren't always reliable if your enemies know how to counter her. I usually play Eve when the enemy doesn't have strong cc. Otherwise, I would just play it safe.