If you are having trouble CS'ing, try spreading some auto's out along the melee, or the caster minions. If you chose melee, go to the side and hit them with a q so it shatters and clears the melee minions for you. If you did the caster minions, hit one of the melee minions head on so q shatters and clears the caster minions. Make use of her passive well, know which spell is more valuable to use at which time, usually the higher mana cost one depending how you rank your abilities. At this point there isn't much advice to give, it's really up to you to play her a bit and get a feel for her, then we can give advice that you'd understand better with the context of having played her a bit. I'd say play her a few days and then bump this thread.
Liandry's Torment is good for her. She makes use of all the stats ( AP for ouchies, Health for not splatting in 2 hits, penetration because dmg) And her kit has the slows in it to make use of its Passive very well.