Eve doesn't really have super hard combos to pull off like Lee Sin or Vi. She's more of a thinking person's champion than a high-reflex comboer. However, there are some small things you can do.

1) AFTER slow. I said this before but it's really important to remember to do this. It means the difference for a kill almost every time, since your spells are like all melee range.

2) on the right target. This one's tough. Remember it pretty much always hits the closest person, so you have to position yourself in melee range. Or, make it so they are between you and any enemy creeps.

3) take advantage of the AS. A lot of people don't even know you get ASPD from this spell, but it's important to know that you do. First of all, when jungling make sure you don't kite the buff while you have ravage on - get your attacks in. Second, when ganking, keep in mind you have really high attack speed after using ravage so try to attack more than moving-wit-hatespike when ganking. In teamfight I wouldn't bother, but it can mean the difference in level 3-5 ganks.

4) don't get spotted too early. This one is important. The yellow eye means they can't see you yet, the red exclamation point means they can. Abuse the maximum range so as to be as close as possible without being seen. This also lets you gank from really weird angles. For instance, people expect a gank from the side brushes, or maybe a jungle entrance. But when you show up right in the middle of the lane behind them, maybe even in a brush, their heads just explode.

5) This was covered in the last section, but do remember that landing good ults is half of what makes a good eve player (the other half being roaming power). You basically have two ways to win the game for your team, and this is one of them!