I've played Eve since I started a couple days ago, and although I was doing decent, I wasn't doing as well as I thought I could. Than I looked and found this guide for her by MrCygnus.
After reading through it and trying it out, I was amazed at how much better I became with her, and kept refining my own efforts to be as effective as possible.
Granted, if the enemy team is in 5 man run around mode and the tank (my cases it's usually Alistar) than your role is diminished greatly; but once someone lags behind, or goes off to nab the golem/lizard buff, or your allies have them occupied by eiter killing them or getting killed, you can pop in and destroy.
A little earlier today my team was getting rolled (partly because early on we fell behind and two people left, but eh, ya keep fighting until it's over for sure.) I did what I always did, assassinating at will, until I got up to the Crystal Rod. From there, I somehow (and I really don't know how I did it) ran in, ganked Veigar in about two seconds, kept truckin' and killed Morgana before the remaining three (Alistar, Master Yi and Nunu) realizied what was happening and turned around and started bashing my face in.
I killed all three of them, just running around randomly spamming Hate Spike and my ult right after one of them died, using Ravage whenever I could, and popped Ignite on Alistar for more dps.
Still lost in the end, but it was a hell of a lot of fun; they bought Oracle Pots afterwards and they still couldn't pin me down until the end, had a 17 kill streak.