You play her like a bitch, go in attack a bit, run out for a little bit, go back in to finish. Resetting your E (empowered by passive) and cleaning up stragglers is her strongsuit. Flanking and wiping out the enemy from unexpected vectors, and annoying them. It's sometimes better to NOT go in and make the enemy botlane scared than to go in at all. Popping my W on Soraka makes her run away from her frontline who was being engaged upon, and with her went the Vayne. Now, it's a 3v4, with them lacking their healer and ADC, their group starts trying to retreat, Soraka and Vayne run up to cover, I open up on the Soraka and they're both retreating too, doing almost no damage, and their entire group is wiped in the blink of an eye.
Evelyn's greatest advantage is her invisibility post-6, the enemy has to respect your potential presence, you can literally walk into a lane, W someone, walk out and head off to a different lane, farm, get objectives, etc. and that laner plays paranoid for a bit. Do it a second time, but this time skirt them, get behind them, wait out your W, and then pop it on them again, this time going for the gank.
Now they don't know what to think, where you will be, or your strategy. She is good at counter-jungling as she can avoid all wards that are placed, and sees red wards that are down (so that she can remove those too). If the enemy jungler or laners want to protect their monsters, they are going to struggle to do so. Regular wards will at best only let them know when you reveal yourself, and unless they are visually watching the area, they won't notice the W on the monster before you uncamo. It's extremely efficient. She lacks a lot of upfront and staying power, she's still an assassin after all. You have to play to mess with their minds if you intend to play her correctly.